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?

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

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.

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

24)(5.040)( 2

+=-=

xxCxxxR

2365.0)( 2 -+-= xxxP

10

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

xxt51

56 4

21 2 -++=

𝑡 =𝑥% + 4�

2+6 − 𝑥5

or

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

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

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

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=

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

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

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

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

=

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

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