Question 1

Sketch the graph of the function   using the curve-sketching guidelines.

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

You are given the graph of a function f. Determine the intervals where the graph of f is concave upward and where it is concave downward.Find all inflection points of f.

Accepted Answer

The answer of You are given the graph of a...

Question 4

You are given the graph of the second derivative   of a function f. 
 
(a) Determine the intervals where the graph of f is concave upward and where it is concave downward.(b) Find the x-coordinates all inflection points of f.

Accepted Answer

The answer of You are given the graph of the...

Question 5

A rectangular beam will be cut from a cylindrical log of radius   inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.

Accepted Answer

A)    in,   in 
B)    in,   in 
C)    in,   in 
D)    in,   in 
E)    in,   in 
A)    in,   in 
B)    in,   in 
C)    in,   in 
D)    in,   in 
E)    in,   in

Question 6

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   and   , IP   and   
B) CU on   and   , CD on   , IP   and   
C) CU on   , IP none 
D) CD on   , IP none 
A) CU on   , CD on   and   , IP   and   
B) CU on   and   , CD on   , IP   and   
C) CU on   , IP none 
D) CD on   , IP none

Question 7

Find the critical numbers of the function.

Accepted Answer

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

Question 8

Find f.

Accepted Answer

The answer of Find f. 
 ...

Question 9

How many real roots does the equation   have in the interval   ?

Accepted Answer

A) no real roots 
B) at most one real root 
C) at most five real roots 
D) at most three real roots 
E) at most two real roots 
A) no real roots 
B) at most one real root 
C) at most five real roots 
D) at most three real roots 
E) at most two real roots

Question 10

Estimate the value of   by using three iterations of Newton's method to solve the equation   with initial estimate   Round your final estimate to four decimal places.

Accepted Answer

A) 1.71 
B) 2.2662 
C) 2.2361 
D) 1.6535 
A) 1.71 
B) 2.2662 
C) 2.2361 
D) 1.6535

Question 11

Find the local and absolute extreme values of the function on the given interval.   ,

Accepted Answer

The answer of Find the local and absolute extreme values...

Question 12

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 13

A woman is on a lake in a rowboat located one mile form the closest point P of a straight shoreline (see the figure). She wishes to get to point Q, 8 miles along the shore from P, by rowing to a point R between P and Q and then walking the rest of the distance. If she can row at a speed of 3 mph and walk at a speed of 4 mph, how should she pick the point R to get to Q as quickly as possible? How much time does she require?
 
    8 mi

Accepted Answer

Question 14

Select the correct graph for the given function   .

Accepted Answer

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

Question 15

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is   ft, find the dimensions of the window so that the greatest possible amount of light is admitted.

Accepted Answer

The answer of A Norman window has the shape of...

Question 16

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 17

Find the dimensions of a rectangle of area 400   that has the smallest possible perimeter.

Accepted Answer

A) 4 ft by 100 ft 
B) 1 ft by 400 ft 
C) 20 ft by 20 ft 
D) 2 ft by 200 ft 
A) 4 ft by 100 ft 
B) 1 ft by 400 ft 
C) 20 ft by 20 ft 
D) 2 ft by 200 ft

Question 18

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

Accepted Answer

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

Question 19

Find the most general antiderivative of the function.

Accepted Answer

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

Question 20

The function   satisfies the hypotheses of the Mean Value Theorem on the interval   . Find all values of c that satisfy the conclusion of the theorem.

Accepted Answer

A) 7 
B) 6 
C) 5, 6 
D) 5, 7 
A) 7 
B) 6 
C) 5, 6 
D) 5, 7

Sketch the graph of the function using the curve-sketching guidelines.

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

You are given the graph of a function f. Determine the intervals where the graph of f is concave upward and where it is concave downward.Find all inflection points of f.

You are given the graph of the second derivative of a function f. (a) Determine the intervals where the graph of f is concave upward and where it is concave downward.(b) Find the x-coordinates all inflection points of f.

A rectangular beam will be cut from a cylindrical log of radius inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.

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 critical numbers of the function.

Find f.

How many real roots does the equation have in the interval ?

Estimate the value of by using three iterations of Newton's method to solve the equation with initial estimate Round your final estimate to four decimal places.

Find the local and absolute extreme values of the function on the given interval. ,

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

Select the correct graph for the given function .

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is ft, find the dimensions of the window so that the greatest possible amount of light is admitted.

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?

Find the dimensions of a rectangle of area 400 that has the smallest possible perimeter.

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

Find the most general antiderivative of the function.

The function satisfies the hypotheses of the Mean Value Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.

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

Sketch the graph of the function using the curve-sketching guidelines.

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

You are given the graph of a function f. Determine the intervals where the graph of f is concave upward and where it is concave downward.Find all inflection points of f.

You are given the graph of the second derivative of a function f. (a) Determine the intervals where the graph of f is concave upward and where it is concave downward.(b) Find the x-coordinates all inflection points of f.

A rectangular beam will be cut from a cylindrical log of radius inches. Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth. Find the dimensions of the strongest beam that can be cut from the cylindrical log.

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 critical numbers of the function.

Find f.

How many real roots does the equation have in the interval ?

Estimate the value of by using three iterations of Newton's method to solve the equation with initial estimate Round your final estimate to four decimal places.

Find the local and absolute extreme values of the function on the given interval. ,

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

Select the correct graph for the given function .

A Norman window has the shape of a rectangle surmounted by a semicircle. (Thus the diameter of the semicircle is equal to the width of the rectangle.) If the perimeter of the window is ft, find the dimensions of the window so that the greatest possible amount of light is admitted.

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?

Find the dimensions of a rectangle of area 400 that has the smallest possible perimeter.

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

Find the most general antiderivative of the function.

The function satisfies the hypotheses of the Mean Value Theorem on the interval . Find all values of c that satisfy the conclusion of the theorem.

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