Question 1

Find the points of inflection and discuss the concavity of the function.

Accepted Answer

A) inflection point at   ; concave downward on   ; concave upward on   
B) inflection point at   ; concave upward on   ; concave downward on   
C) inflection point at   ; concave downward on   ; concave upward on   
D) inflection point at   ; concave upward on   ; concave downward on   
E) inflection point at   ; concare downward on   ; concave upward on   
A) inflection point at   ; concave downward on   ; concave upward on   
B) inflection point at   ; concave upward on   ; concave downward on   
C) inflection point at   ; concave downward on   ; concave upward on   
D) inflection point at   ; concave upward on   ; concave downward on   
E) inflection point at   ; concare downward on   ; concave upward on

Question 2

Identify the open intervals where the function   is increasing or decreasing.

Accepted Answer

A) decreasing:   ; increasing:   
B) increasing:   ; decreasing:   
C) increasing on   
D) decreasing on   
E) decreasing on   ; increasing on   
A) decreasing:   ; increasing:   
B) increasing:   ; decreasing:   
C) increasing on   
D) decreasing on   
E) decreasing on   ; increasing on

Question 3

The measurement of the side of a square floor tile is 20 inches, with a possible error of   inch. Use differentials to approximate the possible propagated error in computing the area of the square.

Accepted Answer

A)    square inches 
B)    square inches 
C)    square inches 
D)    square inches 
E)    square inches 
A)    square inches 
B)    square inches 
C)    square inches 
D)    square inches 
E)    square inches

Question 4

Sketch the graph of the relation   using any extrema, intercepts, symmetry, and asymptotes.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 5

Find the limit.

Accepted Answer

A)    
B)    
C) 0 
D)    
E) -4 
A)    
B)    
C) 0 
D)    
E) -4

Question 6

Find the limit.

Accepted Answer

A) 8 
B)    
C)    
D) 1 
E)    
A) 8 
B)    
C)    
D) 1 
E)

Question 7

The graph of f is shown. Graph f, f' and f'' on the same set of coordinate axes.

Accepted Answer

A)    
B)    
C)    
D)    
E) none of the above 
A)    
B)    
C)    
D)    
E) none of the above

Question 8

Find the value of the derivative (if it exists) of the function   at the extremum point (0,0).

Accepted Answer

A) 0 
B) 1 
C) -1 
D)    
E)    
A) 0 
B) 1 
C) -1 
D)    
E)

Question 9

A rectangular page is to contain   square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 10

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 13 cubic centimeters. Find the radius, r, of the cylinder that produces the minimum surface area. Round your answer to two decimal places.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 11

Find any critical numbers of the function   , t < 4.

Accepted Answer

A) 0 
B)    
C)    
D)    
E)    
A) 0 
B)    
C)    
D)    
E)

Question 12

Use the following graph of   to sketch a graph of f.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 13

The graph of f is shown in the figure. Sketch a graph of the derivative of f.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 14

Locate the absolute extrema of the function   on the closed interval [0,6].

Accepted Answer

A) absolute max: (6, 144) ; absolute min: (2, -16) 
B) absolute max: (2, -16) ; absolute min: (6, 144) 
C) absolute max: (6, 144) ; no absolute min 
D) no absolute max; Absolute min: (6, 144) 
E) no absolute max or min 
A) absolute max: (6, 144) ; absolute min: (2, -16) 
B) absolute max: (2, -16) ; absolute min: (6, 144) 
C) absolute max: (6, 144) ; no absolute min 
D) no absolute max; Absolute min: (6, 144) 
E) no absolute max or min

Question 15

A company introduces a new product for which the number of units sold S is   where t is the time in months since the product was introduced. Find the average value of   during the first year.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 16

Find the limit.

Accepted Answer

A) -3 
B)    
C)    
D) 7 
E) 3 
A) -3 
B)    
C)    
D) 7 
E) 3

Question 17

A model for the average typing speeds S (words per minute) of a typing student after t weeks of lessons is given by   Find

Accepted Answer

A) 96 words per minute 
B) 24 words per minute 
C) 52 words per minute 
D) 104 words per minute 
E) 16 words per minute 
A) 96 words per minute 
B) 24 words per minute 
C) 52 words per minute 
D) 104 words per minute 
E) 16 words per minute

Question 18

Determine the open intervals on which the graph of the function   is concave upward or concave downward.

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 19

Determine the open intervals on which the graph of   is concave downward or concave upward.

Accepted Answer

A) concave downward on   ; concave upward on   
B) concave upward on   
C) concave downward on   
D) concave upward on   ; concave downward on   
E) concave downward on   ; concave upward on   
A) concave downward on   ; concave upward on   
B) concave upward on   
C) concave downward on   
D) concave upward on   ; concave downward on   
E) concave downward on   ; concave upward on

Question 20

Analyze and sketch a graph of the function   .

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Find the points of inflection and discuss the concavity of the function.

Identify the open intervals where the function is increasing or decreasing.

The measurement of the side of a square floor tile is 20 inches, with a possible error of inch. Use differentials to approximate the possible propagated error in computing the area of the square.

Sketch the graph of the relation using any extrema, intercepts, symmetry, and asymptotes.

Find the limit.

Find the limit.

The graph of f is shown. Graph f, f' and f'' on the same set of coordinate axes.

Find the value of the derivative (if it exists) of the function at the extremum point (0,0).

A rectangular page is to contain square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 13 cubic centimeters. Find the radius, r, of the cylinder that produces the minimum surface area. Round your answer to two decimal places.

Find any critical numbers of the function , t < 4.

Use the following graph of to sketch a graph of f.

The graph of f is shown in the figure. Sketch a graph of the derivative of f.

Locate the absolute extrema of the function on the closed interval [0,6].

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced. Find the average value of during the first year.

Find the limit.

A model for the average typing speeds S (words per minute) of a typing student after t weeks of lessons is given by Find

Determine the open intervals on which the graph of the function is concave upward or concave downward.

Determine the open intervals on which the graph of is concave downward or concave upward.

Analyze and sketch a graph of the function .

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters

Exam 6: Applications of Differentiation

Find the points of inflection and discuss the concavity of the function.

Identify the open intervals where the function is increasing or decreasing.

The measurement of the side of a square floor tile is 20 inches, with a possible error of inch. Use differentials to approximate the possible propagated error in computing the area of the square.

Sketch the graph of the relation using any extrema, intercepts, symmetry, and asymptotes.

Find the limit.

Find the limit.

The graph of f is shown. Graph f, f' and f'' on the same set of coordinate axes.

Find the value of the derivative (if it exists) of the function at the extremum point (0,0).

A rectangular page is to contain square inches of print. The margins on each side are 1 inch. Find the dimensions of the page such that the least amount of paper is used.

A solid is formed by adjoining two hemispheres to the ends of a right circular cylinder. The total volume of the solid is 13 cubic centimeters. Find the radius, r, of the cylinder that produces the minimum surface area. Round your answer to two decimal places.

Find any critical numbers of the function , t < 4.

Use the following graph of to sketch a graph of f.

The graph of f is shown in the figure. Sketch a graph of the derivative of f.

Locate the absolute extrema of the function on the closed interval [0,6].

A company introduces a new product for which the number of units sold S is where t is the time in months since the product was introduced. Find the average value of during the first year.

Find the limit.

A model for the average typing speeds S (words per minute) of a typing student after t weeks of lessons is given by Find

Determine the open intervals on which the graph of the function is concave upward or concave downward.

Determine the open intervals on which the graph of is concave downward or concave upward.

Analyze and sketch a graph of the function .

Prerequisites

Functions and Their Graphs

Polynomial and Rational Functions

Limits and Their Properties

Differentiation

Integration

Exponential and Logarithmic Functions

Exponential and Logarithmic Functions and Calculus

Trigonometric Functions

Analytic Trigonometry

Trigonometric Functions and Calculus

Topics in Analytic Geometry

Additional Topics in Trigonometry

Filters