Question 1

Find all the critical numbers of the function.

Accepted Answer

The answer of Find all the critical numbers of the...

Question 2

A rectangular box having a top and a square base is to be constructed at a cost of $1. If the material for the bottom costs $0.35 per square foot, the material for the top costs $0.15 per square foot, and the material for the sides costs $0.20 per square foot, find the dimensions and volume of the box of maximum volume that can be constructed.

Accepted Answer

The answer of A rectangular box having a top and...

Question 3

Find all the maximum and minimum values of the function.

Accepted Answer

The answer of Find all the maximum and minimum values...

Question 4

For what values of c does the curve have maximum and minimum points?

Accepted Answer

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

Question 5

The quantity demanded per month of an item is related to the unit price by the demand equation   ,   where p is measured in dollars and x is measured in units of a thousand. How many items must be sold by the manufacturer to maximize its revenue? Hint: Recall that the revenue is given by

Accepted Answer

The answer of The quantity demanded per month of an...

Question 6

Find the absolute maximum and absolute minimum values, if any, of the function   on   .

Accepted Answer

A) Abs.max.   abs.min.   
B) Abs.max.   abs.min.   
C) Abs.max.   abs.min.   
D) Abs.max.   abs.min.   
A) Abs.max.   abs.min.   
B) Abs.max.   abs.min.   
C) Abs.max.   abs.min.   
D) Abs.max.   abs.min.

Question 7

Find the critical number(s), if any, of the function   .

Accepted Answer

A)    
B) None 
C)    
D)    
A)    
B) None 
C)    
D)

Question 8

Find the critical number(s) of the function.

Accepted Answer

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

Question 9

An efficiency study showed that the total number of cell phones assembled by the average worker at a manufacturing company t hours after starting work at 8 a.m.is given by   
Sketch the graph of the function N, and interpret your result.

Accepted Answer

@#IMG-DLM&
The average worker’

Question 10

A production editor decided that a promotional flyer should have a 1-in. margin at the top and the bottom, and a   -in. margin on each side. The editor further stipulated that the flyer should have an area of 288   . Determine the dimensions of the flyer that will result in the maximum printed area on the flyer.

Accepted Answer

A)    in.     in. 
B)    in.     in. 
C) 12 in.   24 in. 
D) 6 in.   48 in. 
A)    in.     in. 
B)    in.     in. 
C) 12 in.   24 in. 
D) 6 in.   48 in.

Question 11

Estimate the absolute minimum value of the function   to two decimal places on the interval   .

Accepted Answer

The answer of Estimate the absolute minimum value of the...

Question 12

Find the slant asymptote of the graph of   using the curve-sketching guidelines.

Accepted Answer

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

Question 13

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

Accepted Answer

A) CU on   , CD on   , IP   
B) CU on   , CD on   , IP   
C) CU on   , CD on   and   IP   and   
D) CU on   , CD on   , IP   
A) CU on   , CD on   , IP   
B) CU on   , CD on   , IP   
C) CU on   , CD on   and   IP   and   
D) CU on   , CD on   , IP

Question 14

Find the dimensions of the rectangle enclosed in the semicircle   with the largest possible area.

Accepted Answer

A)    in.     in. 
B) 5 in.   7 in. 
C)    in.     in. 
D)    in.     in. 
A)    in.     in. 
B) 5 in.   7 in. 
C)    in.     in. 
D)    in.     in.

Question 15

Find the most general antiderivative of the function.

Accepted Answer

The answer of Find the most general antiderivative of the...

Question 16

The graph of the second derivative   of a function f is shown. State the x-coordinates of the inflection points of 
f.

Accepted Answer

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

Question 17

Find the point on the line   that is closest to the origin.

Accepted Answer

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

Question 18

A car braked with a constant deceleration of   , producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Accepted Answer

The answer of A car braked with a constant deceleration...

Question 19

Sketch the curve.

Accepted Answer

A)    
B)    
C)    
A)    
B)    
C)

Question 20

Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at   is   , find f (1) .

Accepted Answer

A) 11 
B) 1 
C) 0 
D) 12 
E) 6 
A) 11 
B) 1 
C) 0 
D) 12 
E) 6

Find all the critical numbers of the function.

Find all the maximum and minimum values of the function.

For what values of c does the curve have maximum and minimum points?

The quantity demanded per month of an item is related to the unit price by the demand equation , where p is measured in dollars and x is measured in units of a thousand. How many items must be sold by the manufacturer to maximize its revenue? Hint: Recall that the revenue is given by

Find the absolute maximum and absolute minimum values, if any, of the function on .

Find the critical number(s), if any, of the function .

Find the critical number(s) of the function.

An efficiency study showed that the total number of cell phones assembled by the average worker at a manufacturing company t hours after starting work at 8 a.m.is given by Sketch the graph of the function N, and interpret your result.

Estimate the absolute minimum value of the function to two decimal places on the interval .

Find the slant asymptote of the graph of using the curve-sketching guidelines.

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

Find the dimensions of the rectangle enclosed in the semicircle with the largest possible area.

Find the most general antiderivative of the function.

The graph of the second derivative of a function f is shown. State the x-coordinates of the inflection points of f.

Find the point on the line that is closest to the origin.

A car braked with a constant deceleration of , producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Sketch the curve.

Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at is , find f (1) .

Functions and Limits

Derivatives

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

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Exam 3: Applications of Differentiation

Find all the critical numbers of the function.

Find all the maximum and minimum values of the function.

For what values of c does the curve have maximum and minimum points?

The quantity demanded per month of an item is related to the unit price by the demand equation , where p is measured in dollars and x is measured in units of a thousand. How many items must be sold by the manufacturer to maximize its revenue? Hint: Recall that the revenue is given by

Find the absolute maximum and absolute minimum values, if any, of the function on .

Find the critical number(s), if any, of the function .

Find the critical number(s) of the function.

An efficiency study showed that the total number of cell phones assembled by the average worker at a manufacturing company t hours after starting work at 8 a.m.is given by Sketch the graph of the function N, and interpret your result.

Estimate the absolute minimum value of the function to two decimal places on the interval .

Find the slant asymptote of the graph of using the curve-sketching guidelines.

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

Find the dimensions of the rectangle enclosed in the semicircle with the largest possible area.

Find the most general antiderivative of the function.

The graph of the second derivative of a function f is shown. State the x-coordinates of the inflection points of f.

Find the point on the line that is closest to the origin.

A car braked with a constant deceleration of , producing skid marks measuring 500 ft before coming to a stop. How fast was the car traveling when the brakes were first applied?

Sketch the curve.

Given that the graph of f passes through the point (4, 69) and that the slope of its tangent line at is , find f (1) .

Functions and Limits

Derivatives

Integrals

Applications of Integration

Inverse Functions

Techniques of Integration

Further Applications of Integration

Differential Equations

Parametric Equations and Polar Coordinates

Infinite Sequences and Series

Vectors and the Geometry of Space

Vector Functions

Partial Derivatives

Multiple Integrals

Vector Calculus

Second-Order Differential Equations

Final Exam

Filters