Question 1

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

Question 2

Find the most general antiderivative of the function.

Accepted Answer

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

Question 3

Find two positive numbers whose product is   and whose sum is a minimum.

Accepted Answer

A)    
B) 3, 48 
C)    
D) 6, 24 
E) 2, 72 
A)    
B) 3, 48 
C)    
D) 6, 24 
E) 2, 72

Question 4

Find the absolute maximum and absolute minimum values, if any, of the function   on [0, 25]

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 5

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 6

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

Accepted Answer

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 
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

Question 7

Find the position function of a particle moving along a coordinate line that satisfies the given conditions.   , s (0) = 5, v (0) = 0

Accepted Answer

The answer of Find the position function of a particle...

Question 8

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem.   ,

Accepted Answer

A) None of these 
B)    ,   
C)    ,   
D)    ,   
E)    ,   
A) None of these 
B)    ,   
C)    ,   
D)    ,   
E)    ,

Question 9

Find all the critical numbers of the function.

Accepted Answer

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

Question 10

At 4:00 P.M. a car's speedometer reads 25   . At 4:15 it reads 72   . At some time between 4:00 and 4:15 the acceleration is exactly x   . Find x.

Accepted Answer

The answer of At 4:00 P.M. a car's speedometer reads...

Question 11

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

Accepted Answer

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

Question 12

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

Accepted Answer

absolute m

Question 13

The function   satisfies the hypotheses of Rolle's Theorem on the interval   . Find all values of c that satisfy the conclusion of the theorem.

Accepted Answer

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

Question 14

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 15

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

Accepted Answer

A)    
B)    
C) None of these 
D)    
A)    
B)    
C) None of these 
D)

Question 16

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

Accepted Answer

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

Question 17

Use Newton's method to approximate the given number correct to eight decimal places.

Accepted Answer

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

Question 18

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

Accepted Answer

A)    
B)    
C) -4 
D)    
A)    
B)    
C) -4 
D)

Question 19

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

Accepted Answer

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.   
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.

Question 20

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

Accepted Answer

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.   
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.

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) .

Find the most general antiderivative of the function.

Find two positive numbers whose product is and whose sum is a minimum.

Find the absolute maximum and absolute minimum values, if any, of the function on [0, 25]

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?

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

Find the position function of a particle moving along a coordinate line that satisfies the given conditions. , s (0) = 5, v (0) = 0

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. ,

Find all the critical numbers of the function.

At 4:00 P.M. a car's speedometer reads 25 . At 4:15 it reads 72 . At some time between 4:00 and 4:15 the acceleration is exactly x . Find x.

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

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

The function satisfies the hypotheses of Rolle's Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.

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

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

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

Use Newton's method to approximate the given number correct to eight decimal places.

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

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.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters

Exam 4: Applications of Differentiation

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) .

Find the most general antiderivative of the function.

Find two positive numbers whose product is and whose sum is a minimum.

Find the absolute maximum and absolute minimum values, if any, of the function on [0, 25]

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?

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

Find the position function of a particle moving along a coordinate line that satisfies the given conditions. , s (0) = 5, v (0) = 0

Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval. Then find all numbers c that satisfy the conclusion of Rolle's Theorem. ,

Find all the critical numbers of the function.

At 4:00 P.M. a car's speedometer reads 25 . At 4:15 it reads 72 . At some time between 4:00 and 4:15 the acceleration is exactly x . Find x.

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

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

The function satisfies the hypotheses of Rolle's Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.

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

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

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

Use Newton's method to approximate the given number correct to eight decimal places.

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

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.

Functions and Limits

Derivatives

Inverse Functions: Exponential, Logarithmic, and Inverse Trigonometric Functions

Integrals

Techniques of Integration

Applications of Integration

Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Partial Derivatives

Multiple Integrals

Vector Calculus

Filters