Question 1

Use the guidelines of this section to sketch the curve.  Select the graph of the curve.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the guidelines of this section to...

Question 2

What is the minimum vertical distance between the parabolas  and  ?

Accepted Answer

The answer of What is the minimum vertical distance between...

Question 3

Use the guidelines of this section to sketch the curve.  Select the graph of the curve.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the guidelines of this section to...

Question 4

A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner?

Accepted Answer

The answer of A steel pipe is being carried down...

Question 5

Given  .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of f.
A)(a) Increasing on  ,
Decreasing on

(b) Rel. max. 
B)(a) Increasing on 
(b) None
C)(a) Decreasing on 
(b) None
D)(a) Increasing on  ,
Decreasing on

(b) Rel. min.

Accepted Answer

The answer of Given  .(a) Find the intervals on...

Question 6

The graph of the derivative  of a continuous function f is shown. On what intervals is f decreasing?  .
A) 
B) 
C) 
D) 
E)None of these

Accepted Answer

The answer of The graph of the derivative  of...

Question 7

Use the guidelines of this section to sketch the curve.  Select the graph of the curve.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the guidelines of this section to...

Question 8

Determine where the graph of the function  is concave upward and where it is concave downward. Also, find all inflection points of the function.
A)CU on  , CD on
 ,
IP

B)CU on  , CD on
 ,
IP

C)CU on  , CD on
 ,
IP

D)CU on  , CD on
 ,
IP

Accepted Answer

The answer of Determine where the graph of the function...

Question 9

Use the guidelines of this section to sketch the curve.  Select the graph of the curve.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the guidelines of this section to...

Question 10

Find an equation of the line through the point  that cuts off the least area from the first quadrant.

Accepted Answer

The answer of Find an equation of the line through...

Question 11

Find the maximum or minimum point(s) of the function. 
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Find the maximum or minimum point(s) of...

Question 12

Determine where the graph of  is concave upward and where it is concave downward. Also, find all inflection points of the function.
A)concave downward:  and
 , concave upward:
 and
 ; inflection points:
 and

B)concave downward:  and
 , concave upward:
 and
 ; inflection points:
 and

C)concave downward: nowhere, concave upward:  and
 ; inflection points: none
D)concave downward:  and
 , concave upward: nowhere; inflection points: none

Accepted Answer

The answer of Determine where the graph of  is...

Question 13

A farmer with 710 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

Accepted Answer

The answer of A farmer with 710 ft of fencing...

Question 14

Given  .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of f.
A)(a) Increasing on  ,
Decreasing on

(b) Rel. max. 
B)(a) Increasing on  ,
Decreasing on

(b) Rel. min. 
C)(a) Increasing on  ,
Decreasing on

(b) Rel. max. 
D)(a) Increasing on  ,
Decreasing on

(b) Rel. min.

Accepted Answer

The answer of Given  .(a) Find the intervals on...

Question 15

Given  .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of f.
A)(a) Increasing on  and
 , decreasing on

(b) Rel. max.  ,
Rel) min. 
B)(a) Increasing on  and
 , decreasing on
 and

(b) Rel. max.  ,
Rel) min. 
C)(a) Increasing on  , decreasing on
 and

(b) Rel. max.  ,
Rel) min. 
D)(a) Increasing on  and
 decreasing on
 and

(b) Rel. max.  ,
Rel) min.

Accepted Answer

The answer of Given  .(a) Find the intervals on...

Question 16

Use the guidelines of this section to sketch the curve.  Select the graph of the curve.
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Use the guidelines of this section to...

Question 17

Determine where the graph of the function  is concave upward and where it is concave downward. Also, find all inflection points of the function.
A)CU on  , CD on
 ,
IP

B)CU on  , CD on
 and

IP
 and

C)CU on  , CD on
 ,
IP

D)CU on  , CD on
 ,
IP

Accepted Answer

The answer of Determine where the graph of the function...

Question 18

Use the Second Derivative Test to find the relative extrema, if any, of the function  .
A)Rel. max.  , rel. min. 
B)Rel. max.  , rel. min. 
C)Rel. max.  , rel. min. 
D)Rel. max.  , rel. min.

Accepted Answer

The answer of Use the Second Derivative Test to find...

Question 19

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L = 8 and width W = 3.

Accepted Answer

The answer of Find the maximum area of a rectangle...

Question 20

Given  .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of f.
A)(a) Increasing on  and
 decreasing on

(b) Rel. max.  ,
Rel) min. 
B)(a) Increasing on  , decreasing on
 and

(b) Rel. max.  ,
Rel) min. 
C)(a) Increasing on  and
 decreasing on

(b) Rel. max.  ,
Rel) min. 
D)(a) Increasing on  , decreasing on
 and

(b) Rel. max.  ,
Rel) min.

Accepted Answer

The answer of Given  .(a) Find the intervals on...

Quiz 4: Applications of Differentiation

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

What is the minimum vertical distance between the parabolas and ?

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

A steel pipe is being carried down a hallway 14 ft wide. At the end of the hall there is a right-angled turn into a narrower hallway 6 ft wide. What is the length of the longest pipe that can be carried horizontally around the corner?

Given .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of f.

The graph of the derivative of a continuous function f is shown. On what intervals is f decreasing? .

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

Determine where the graph of the function is concave upward and where it is concave downward. Also, find all inflection points of the function.

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

Find an equation of the line through the point that cuts off the least area from the first quadrant.

Find the maximum or minimum point(s) of the function.

Determine where the graph of is concave upward and where it is concave downward. Also, find all inflection points of the function.

A farmer with 710 ft of fencing wants to enclose a rectangular area and then divide it into four pens with fencing parallel to one side of the rectangle. What is the largest possible total area of the four pens?

Given .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of f.

Given .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of f.

Use the guidelines of this section to sketch the curve. Select the graph of the curve.

Determine where the graph of the function is concave upward and where it is concave downward. Also, find all inflection points of the function.

Use the Second Derivative Test to find the relative extrema, if any, of the function .

Find the maximum area of a rectangle that can be circumscribed about a given rectangle with length L = 8 and width W = 3.

Given .(a) Find the intervals on which f is increasing or decreasing.(b) Find the relative maxima and relative minima of f.