1 review review test 2. 2 1. find the derivative for y = 3x 2 + 5x - 7 a. y’ = 3x + 5c. y’ = 6x...
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![Page 1: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/1.jpg)
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REVIEWTEST 2
![Page 2: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/2.jpg)
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1. Find the derivative fory = 3x 2 + 5x - 7
A. y’ = 3x + 5 C. y’ = 6x
C. y’ = 6x + 5 D. y’ = 6x + 5 - 7
E. None of the above
![Page 3: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/3.jpg)
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No that answer is incorrect.
You need to use the power rule on each of the terms of the equation.
The power rule is –
If y = x n , then y’ = n x n – 1 .
Please click here to try again.
![Page 4: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/4.jpg)
4
Yes, the answer is y’ = 6x + 5
Please click here for the next question.
Good work on using the power rule!
If y = x n , then y’ = n x n – 1 .
![Page 5: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/5.jpg)
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2. Find the derivative fory = 2x – 1 – x – 3
A. y’ = - 2x 0 + 3x – 2 B. y’ = -2x – 2 – 3x – 4
C. y’ = 2x – 2 + 3x – 4 D. y’ = - 2x – 2 + 3x – 4
E. None of the above
![Page 6: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/6.jpg)
6
No that answer is incorrect.
You need to use the power rule on each of the terms of the equation.
The power rule is –
If y = x n , then y’ = n x n – 1 .
Watch your negative signs!
Please click here to try again.
![Page 7: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/7.jpg)
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Yes, the answer is y’ = - 2x – 2 + 3x – 4
Please click here for the next question.
Good work on using the power rule!
If y = x n , then y’ = n x n – 1 .
![Page 8: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/8.jpg)
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3. Find the derivative fory = (2x 2 – x + 1)(x – 2)
A. y’ = (4x – 1)(1)
B. y’ = 6x 2 - 10x + 3
C. y’ = (2x 2 – x + 1)(1) + (x – 2)(4x – 1)
D. y’ = (4x – 1)(x - 1)
E. None of the above
![Page 9: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/9.jpg)
9
Too bad that answer is incorrect.
You need to use the product rule.
Please click here to try again.
The product rule is –
If f (x) = F (x) • S (x),
Then f ’ (x) = F (x) • S’ (x) + S (x) • F ’(x)
![Page 10: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/10.jpg)
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Yes, the answer is y’ = 6x 2 - 10x + 3 or
y’ = (2x 2 – x + 1)(1) + (x – 2)(4x – 1)
Please click here for the next question.
Good work on using the product rule
If y = f · s , then y’ = f · s’ + s · f’ .
![Page 11: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/11.jpg)
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4. Find the derivative for
A.
B. C.
D. y’ = (5x + 2)(2x) – (x 2 + 3) (5)
E. None of the above
2x5
3xy
2
2
2
)2x5(
)5)(3x()x2)(2x5('y
2
2
)2x5(
15x4x5'y
2
2
)2x5(
)5)(3x()x2)(2x5('y
![Page 12: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/12.jpg)
12
Sorry, that answer is incorrect.
Please click here to try again.
You need to use the quotient rule.
The quotient rule is –
If
Then
)x(B
)x(Ty
2])x(B[
)x('B)x(T)x('T)x(B'y
![Page 13: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/13.jpg)
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Great, the correct answer is
Please click here for the next question.
2
2
)2x5(
15x4x5'y
OR
2
2
)2x5(
)5)(3x()x2)(2x5('y
You used the quotient rule correctly!!
)x(B
)x(Ty
2])x(B[
)x('B)x(T)x('T)x(B'y
If then
![Page 14: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/14.jpg)
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5. Find the derivative for
A. y’ = - 2 x 1/2 B. y’ = 4 x – 3/2
C. y’ = - 2 x – 3/2 D. y’ = 4 x 1/2
E. None of the above
x
4y
![Page 15: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/15.jpg)
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Not quite, that answer is incorrect.
Change the equation to remove the radical to –
y = 4x – 1/2
and use the power rule.
Please click here to try again.
![Page 16: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/16.jpg)
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Hey great, the correct answer is y’ = - 2 x – 3/2
Please click here for the next question.
Nice work on the power rule and negative exponents.
![Page 17: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/17.jpg)
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6. Find the derivative for
A. y’ = 5 (x 2 – 3x + 6) 4
B. y’ = (x 2 – 3x + 6) 5 (2x – 3)
C. y’ = (2x - 3) 5
D. y’ = 5 (x 2 – 3x + 6) 4 (2x – 3)
E. None of the above
y = (x 2 – 3x + 6) 5
![Page 18: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/18.jpg)
18
Too bad, that answer is incorrect.
You need to use the chain rule with
u = x 2 – 3x + 6
Please click here to try again.
dx
duunu
dx
d 1nn
![Page 19: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/19.jpg)
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OK, the correct answer is
y’ = 5 (x 2 – 3x + 6) 4 (2x – 3)
Please click here for the next question.
dx
duunu
dx
d 1nn
Good use of the chain rule with
u = x 2 – 3x + 6 !!
![Page 20: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/20.jpg)
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7. Find the derivative for
A. y’ = x (x 2 + 3) – 1/2
B. y’ = (x 2 + 3) – 1/2
D. y’ = 1/2 (x 2 + 3) - ½ (2x)
E. None of the above
3xy 2
C. 3+xx2='y 2
![Page 21: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/21.jpg)
21
Too bad, that answer is incorrect.
You need to rewrite the equation without a radical and then use the chain rule
y = (x 2 + 3) ½ and the let u = x 2 + 3
Please click here to try again.
dx
duunu
dx
d 1nn
![Page 22: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/22.jpg)
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Terrrrriffffic!!
Please click here for the next question.
3x
x'y
2
Rewrite the equation without a radical and then use the chain rule - y = (x 2 + 3) ½ and the let u = x 2 + 3
Then y’ = x (x 2 + 3) – ½ OR
y’ = 1/2 (x 2 + 3) - ½ (2x) OR
![Page 23: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/23.jpg)
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6. If f (x) = 2x 3 - 3x 2 – 5x + 3, find the second derivative.
A. y” = 6x – 6 B. y” = 6x 2
C. y” = 12x - 6 D. y” = 6x 2 - 6x - 5
E. None of the above
![Page 24: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/24.jpg)
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No that answer is incorrect.
You need to take the derivative of the derivative!
Please click here to try again.
![Page 25: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/25.jpg)
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Yes Yes Yes, the correct answer is y” = 12x - 6.
Please click here for the next question.
y’ = 6x 2 - 6x – 5 and
y” = 12x - 6
![Page 26: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/26.jpg)
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APPLICATIONS
Now, let’s try some application problems
![Page 27: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/27.jpg)
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9. A drug is injected into the bloodstream. The concentration of the drug after x hours is given by
A. Find the marginal concentration after 3 hours (4 decimal places).
A. C’ (x) = 0.0462 ml/cm 3
B. C’ (x) = – 0.1746 ml/cm 3
C. C’ (x) = – 0.0059 ml/cm 3
D. C’ (x) = 0.5428 ml/cm 3
E. None of the above
4x
x20.0)x(C
2 for 0 x 10.
![Page 28: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/28.jpg)
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Sorry that answer is incorrect.
To find the marginal concentration graph the given function and under the CALC menu use the dy/dx choice at x = 3.
Please click here to try again.
![Page 29: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/29.jpg)
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Yes, the answer is C’ (x) = – 0.0059 ml/cm 3
from your graphing calculator.
Please click here for the next question.
NOTE: You will need this answer for the next question.
![Page 30: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/30.jpg)
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10. A drug is injected into the bloodstream. The concentration of the drug after x hours is given by
B. Interpret the results of the previous question.
Take a minute and try to write a response.
Go to a representative correct answer.
4x
x20.0)x(C
2 for 0 x 10.
![Page 31: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/31.jpg)
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The drug concentration after three hours is decreasing by about 0.0059 ml/cm 3 for the next hour.
Please click here for the next question.
![Page 32: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/32.jpg)
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11. The total profit from the sale of text books is P (x) = 30 x – 0.3 x 2 - 200 0 ≤ x ≤ 100.
A. Find the marginal profit when x = 40.
A. P’ (x) = 0
B. P’ (x) = – 6
C. P’ (x) = 6
D. P’ (x) = undefined
E. None of the above
![Page 33: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/33.jpg)
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Oooooh too bad that answer is incorrect.
To find the marginal profit consider graphing the function and under the CALC menu use the dy/dx choice at x = 40.
Please click here to try again.
![Page 34: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/34.jpg)
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Yes, the answer is P’ (x) = 6
from your graphing calculator.
Please click here for the next question.
NOTE: You will need this answer for the next question.
![Page 35: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/35.jpg)
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12. B. The total profit from the sale of text books is P (x) = 30 x – 0.3 x 2 - 200 0 ≤ x ≤ 100.
B. Interpret P ‘ (40) = 6
Write an interpretation and then click here to see a representative answer.
![Page 36: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/36.jpg)
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Please click here for the next question.
The profit when selling the next textbook (#41) will increasing by about $6.
![Page 37: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/37.jpg)
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13. The total profit (in dollars) from the sale of x calculators is P (x) = 22x – 0.2x 2 – 400 A. Find the average profit per calculator if 50 calculators are produced and sold.
A. P (x) = $4 B. P (x) = $3
C. P (x) = $3.50 D. P (x) = $2
E. None of the above
for 0 x 100.
![Page 38: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/38.jpg)
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Too bad that answer is incorrect.
The average profit is the profit divided by x. Calculate the profit at 50 and divide by 50. If you wish you can graph the average profit on your calculator and find CALC then VALUE at x = 50.
Please click here to try again.
x
400x2.0x22
x
xP)x(P
2
![Page 39: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/39.jpg)
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Yes, the answer is
Please click here for the next question.
4$50
200
50
400)50)(2.0()50)(22(
50
)50(P)50(P
2
OR
![Page 40: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/40.jpg)
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14. The total profit (in dollars) from the sale of x calculators is P (x) = 22x – 0.2x 2 – 400
B. Find the marginal average profit at a production level of 50 calculators.
A. P’ (x) = $ 0.04
B. P’ (x) = $ - 0.04
C. P’ (x) = $ 0.40
D. P’ (x) = $ - 0.40
E. None of the above
for 0 x 100.
![Page 41: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/41.jpg)
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No that answer is incorrect.
There are several ways to get the marginal average profit. Perhaps the easies is to graph the average profit and go to CALC and dy/dx at 50.
Please click here to try again.
x
400x2.0x22
x
xP)x(PofitPrAvg
2
![Page 42: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/42.jpg)
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Yesaroonie, the answer is – 0.04.
Please click here for the next question.
x
400x2.0x22
x
xP)x(PGraph
2
NOTE: You will need this answer for the next question.
![Page 43: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/43.jpg)
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15. Write a brief interpretation of the results of the previous problem.
Take a minute and write an interpretation.
Go to a representative correct answer.
![Page 44: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/44.jpg)
44
Please click here for the next question.
The average profit is decreasing by about $0.04 for the sale of the 51st calculator.
![Page 45: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/45.jpg)
45
16. The price-demand and cost equations for producing gadgets are given by:
p (x) = (6000 - x)/30 and C (x) = 72000 + 60x for 0 x 6,000. A. Find the revenue function.
A. R (x) = x (6000 - x)/30
B. R (x) = (6000 - x)/(30x)
C. R (x) = x (72000 + 60x)
D. R (x) = p (x) + C (x)
E. None of the above
![Page 46: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/46.jpg)
46
Sorry that answer is incorrect.
To find the revenue function use R (x) = xp, where p is the price-demand function.
Please click here to try again.
![Page 47: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/47.jpg)
47
You have what it takes.
The correct answer is R (x) = xp
= x (6000 - x)/30
Please click here for the next question.
NOTE: You will need this answer for the next question.
![Page 48: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/48.jpg)
48
17. The price-demand and cost equations for producing gadgets are given by:
p (x) = (6000 - x)/30 and C (x) = 72000 + 60x for 0 x 6,000. A. Find the marginal revenue function.
A. R’ (x) = 60000 – x/30
B. R’ (x) = p’ (x) – C’ (x)
C. R’ (x) = 200 – x/15
D. R’ (x) = 200 – x/30
E. None of the above
![Page 49: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/49.jpg)
49
Not the correct answer.
To find the marginal revenue function you need to find the derivative of the revenue function from the previous problem.
R (x) = x (6000 - x)/30
Please click here to try again.
![Page 50: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/50.jpg)
50
Great calculus work.
The correct answer is
the derivative of R (x) = x (6000 - x)/30
Please click here for the next question.
R (x) = x (6000 - x)/30
= 200x – x 2/30 and
R’ (x) = 200 – 2x/30
= 200 – x/15
NOTE: You will need this answer for the next question.
![Page 51: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/51.jpg)
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18. The price-demand and cost equations for producing gadgets are given by:
p (x) = (6000 - x)/30 and C (x) = 72000 + 60x for 0 x 6,000. C. Find the marginal revenue at x = 1500.
A. $25
B. $100
C. $75
D. $125
E. None of the above
![Page 52: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/52.jpg)
52
Sorry incorrect. Try the following hint.
Plug 1500 into the marginal revenue equation (answer to the previous problem) for x and solve for R’ (x),
Please click here to try again.
![Page 53: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/53.jpg)
53
Great work.
The marginal revenue equation is
R’ (x) = 200 – x/15 and
R’ (1500) = 200 – 1500/15
= 200 - 100
= $100
Please click here for the next question.
NOTE: You will need this answer for the next question.
![Page 54: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/54.jpg)
54
19. The price-demand and cost equations for producing gadgets are given by:
p (x) = (6000 - x)/30 and C (x) = 72000 + 60x for 0 x 6,000. D. Write a brief interpretation of the result of the previous problem.
Go ahead, I’ll wait for you.
Click here to see a representative correct answer.
![Page 55: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/55.jpg)
55
Please click here for the next question.
At a sales rate of 1500, the revenue will be about $100 on the sale of the next gadget.
![Page 56: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/56.jpg)
56
20. The price-demand and cost equations for producing gadgets are given by:
p (x) = (6000 - x)/30 and C (x) = 72000 + 60x for 0 x 6,000. E. Find the profit function.
A. P (x) = 260x – x 2/30 - 72000
B. P (x) = C (x) – R (x)
C. P (x) = 140x – x 2/30 - 72000
D. P (x) = 140x – x/30 - 72000
E. None of the above
![Page 57: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/57.jpg)
57
Too bad, that is incorrect.
The profit function is found by subtracting cost from revenue, or
P (x) = R (x) – C (x)
Please click here to try again.
![Page 58: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/58.jpg)
58
Well done!
The correct answer is P (x) = 140x – x 2/30 - 72000
P (x) = R (x) – C (x)
= (200x – x 2/30) – (72000 + 60x)
= 140x – x 2/30 - 72000
Please click here for the next question.
NOTE: You will need this answer for the next question.
![Page 59: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/59.jpg)
59
21. The price-demand and cost equations for producing gadgets are given by:
p (x) = (6000 - x)/30 and C (x) = 72000 + 60x for 0 x 6,000. E. Find the marginal profit function.
A. P’ (x) = 140x – x 2/30 - 72000
B. P’ (x) = 140 – x/30
C. P’ (x) = 140 – x/15
D. P’ (x) = 140x – x/15
E. None of the above
![Page 60: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/60.jpg)
60
Sorry that is incorrect.
The marginal profit is the derivative of the profit and the profit was found in the previous problem.
Please click here to try again.
![Page 61: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/61.jpg)
61
Well done!
The correct answer P’ (x) = 140 – x/15
Please click here for the next question.
Take the derivative of P in the previous problem.
P (x) = 140x – x 2/30 – 72000 and
P’ (x) = 140 – x /15
![Page 62: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/62.jpg)
62
22. A company that makes CD players has the following total cost function.
C (x) = x 2 + 2x + 2000.C. What is the minimum average cost?
A. $ 37.54
B. $ 87.46
C. $ 44.72
D. $ 91.44
E. None of the above
![Page 63: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/63.jpg)
63
No that is incorrect.
Remember the average cost function is the cost divided by x or
Graph the average cost function on your calculator and find the minimum. Use a window of 0 < x < 100 and 0 < y < 200.
Please click here to try again.
x
)x(C)x(C
![Page 64: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/64.jpg)
64
Sorry that is not the correct answer, but it is close.
You were asked for the minimum average cost. You want the y value not the x value.
Please click here to try again.
![Page 65: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/65.jpg)
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Terrific!
The correct answer $91.44.
Please click here for the next question.
Did you use your calculator to find that?
x
)x(C)x(C
x
2000x2x2
0 < x < 100 and 0 < y < 200.
![Page 66: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/66.jpg)
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23 – 25. The price-demand and cost equations for producing gadgets are given by:
p (x) = 270 – 10x and C (x) = 100 + 70x for 0 x 20.
23. How many gadgets should be produced to maximize profit?.
A. 900
B. 10
C. 120
D. 12
E. None of the above.
![Page 67: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/67.jpg)
67
Too bad that is incorrect.This one is a lot of work. From the price equation form the revenue equation; R = xp. Use that revenue equation and the given cost equation to form the profit equation. Use your calculator to maximize the profit.
Please click here to try again.
![Page 68: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/68.jpg)
68
That us close but incorrect.
You gave the maximum profit – you need the x value where the maximum profit occurs.
Please click here to try again.
![Page 69: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/69.jpg)
69Please click here for the next question.
Yes indeedie calculator speedie! X = 6.
Note P(x) = R – C = (x(270 – 10x))-(100 + 70x)
Save this info for #30 and #31.
![Page 70: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/70.jpg)
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23 – 25. The price-demand and cost equations for producing gadgets are given by:
p (x) = 270 – 10x and C (x) = 100 + 70x for 0 x 20.
24. What is the maximize profit?.
A. 900
B. 10
C. 120
D. 12
E. None of the above.
![Page 71: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/71.jpg)
71
Too too too bad that is incorrect.From the previous problem use the profit formula and use your calculator to maximize the profit.
Please click here to try again.
![Page 72: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/72.jpg)
72
Please click here for the next question.
Yes indeedie calculator speedie! X = 6.
Save this info for #31.
![Page 73: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/73.jpg)
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23 – 25. The price-demand and cost equations for producing gadgets are given by:
p (x) = 270 – 10x and C (x) = 100 + 70x for 0 x 20.
25. Now for the really important question – What price should be charged to maximize the profit?.
A. $900
B. $10
C. $170
D. $65.50
E. None of the above.
![Page 74: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/74.jpg)
74
Well consider trying again.
The price equation is given. Use the facts from the previous two problems to determine what x value to substitute into that equation.
Please click here to try again.
![Page 75: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/75.jpg)
75
Please click here for the next question.
Hey, hey, hey, hey, HEY!!!!
Yes you plugged x = 10 into the price equation to get $170 didn’t you. You cleaver devil.
![Page 76: 1 REVIEW REVIEW TEST 2. 2 1. Find the derivative for y = 3x 2 + 5x - 7 A. y’ = 3x + 5C. y’ = 6x C. y’ = 6x + 5D. y’ = 6x + 5 - 7 E. None of the above](https://reader035.vdocuments.mx/reader035/viewer/2022070409/56649e905503460f94b95733/html5/thumbnails/76.jpg)
76
That was a lot of review. I hope you found it helpful. Good luck on the test!