check endpoints on a closed interval, what did you · 2019-11-21 · rate of 5 ft/sec. at what rate...

1

When finding absolute extremaon a closed interval, what did you

promise you would remember?

Check endpoints

When finding critical values, what did you promise you would

remember?

Set derivative to BOOM!

2

Find the critical values.

𝑓" 𝑥 =𝑥% + 2𝑥𝑥% − 9 3

320

-==-=

=

xxxx

Find (if any) the absolute extremaon the interval.

xexf =)( )3 ,2[-Absolute min:Absolute max: none

÷øö

çèæ- 2

1 ,2e

3

Find the absolute extrema of the function on the given interval.

52)( 2 -+= xxxf [ ]2 ,3- Absolute min:Absolute max: )3 ,2(

)6 ,1( --

)(' xfy = To the nearest half,

approximate the x-vals for

each POI 5.31

==xx

4

66''63'

632

23

--=--=

+--=

xyxxyxxy

Find all POINTS of inflection

)4 ,1(-

0)3('0)1('

==-

ff ''f

0=x

+ -

Identify all local extrema.

local min at local max at 3

1=-=

xx

5

1 3

2

v

a

- -

-

+

+

When is Jordan slowing down?

)1 ,0( )3 ,2(and

)(' xfy =Use the graph

of f ` to determine the

location (to the nearest whole

number) of local mins

and/or maxes.

3

61

=

==

x

xx

Local mins

Local max

6

Complete the sentence.

According to MVT, somewhere in the interval [1, 6]…

)(xf is continuous & differentiable,

20)6(35)1(==

ff

3)(' -=xf

124)( 23 +-+= xxxxf

12 +-= xy

The equation of the tangent line to f at the point (0, 1) is

given below. Use it to approximate )01.0(f 98.0)01.0( »f

7

Find the linearization of

atx

xxf 1)( +=

3=a

𝑦 −103=89(𝑥 − 3)

or

𝑦 =89𝑥 +

23

Find the value of c that satisfies the MVT for

on

24)( 2 ++= xxxf

[ ]2 ,3 --

25

-=c

8

Determine if the function satisfies the hypothesis of the MVT.

If not, state the reason.

[ ]1 ,3on 3 -= xy

It does not satisfy the hypothesis of MVT because

it’s not differentiable at which is on 0=x ]1 ,3[-

Of all numbers whose sum is 390, find the two that have the

maximum product.

Write the simplified equation you would differentiate to solve the problem.

2390 xxP -=

9

From a thin piece of cardboard 40 in. by 40 in., square corners are cut out so that the

sides can be folded up to make a box. What dimensions will yield a box of

maximum volume?


𝑉 = 4𝑥3 − 160𝑥% + 1600𝑥

Find the number of units that must be produced and sold in order to yield the maximum profit, given the following

equations for revenue and cost.


24)(5.040)( 2

+=-=

xxCxxxR

2365.0)( 2 -+-= xxxP

10


xxt51

56 4

21 2 -++=

𝑡 =𝑥% + 4�

2+6 − 𝑥5

or


A rectangular sheet of perimeter 32 cm and dimensions x cm by y cm is to be rolled into a cylinder with

circumference x and height y. What values of x and y give the largest

volume?

𝑉 =4𝑥%

𝜋−𝑥3

4𝜋or

𝑉 =14𝜋

𝑦3 −8𝜋𝑦% +

64𝜋𝑦

11


A spherical balloon is inflated with helium at a rate of 110π ft3/min. How fast is the balloon's radius

increasing when the radius is 8 ft ?

3

34 rV p=


A metal cube dissolves in acid such that an edge of the cube decreases by 0.57 mm/min. How fast is the

volume of the cube changing when the edge is 9.7 mm?

3eV =

12


A conical paper cup is 30 cm tall with a radius of 10 cm. The cup is being

filled with water so that the water level (h) rises at a rate of 3/h cm/sec. At what rate if the water being poured into the cup when the water level is

7 cm?

3

27hV p

=


A 13 ft ladder is leaning against a house when the base of the ladder begins to slide away from the house. When the base is 12 ft from the house, the base is moving at a rate of 5 ft/sec. At what rate is the angle

between the ladder and the ground changing at that moment?

13cos x

=q

13

Answer both parts.

(a)

(b)

cm/sec 524

cm/sec 0

check endpoints on a closed interval, what did you · 2019-11-21 · rate of 5 ft/sec. at what rate...

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