Question 1

Find the inflection points for the function given.   ,

Accepted Answer

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

Question 2

Sketch the curve.

Accepted Answer

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

Question 3

Use Newton's method to approximate the indicated root of   in the interval   , correct to six decimal places.
Use   as the initial approximation.

Accepted Answer

The answer of Use Newton's method to approximate the indicated...

Question 4

Find the absolute maximum value of   on the interval   .

Accepted Answer

A) 4 
B) 6 
C) 5 
D) 7 
E) 3 
A) 4 
B) 6 
C) 5 
D) 7 
E) 3

Question 5

Find the maximum and minimum points of the function.

Accepted Answer

The answer of Find the maximum and minimum points of...

Question 6

A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and before deploying her parachute is given by   where   is measured in meters per second. What is her terminal velocity? Hint: Evaluate

Accepted Answer

A)    m/sec 
B)    m/sec 
C)    m/sec 
D)    m/sec 
A)    m/sec 
B)    m/sec 
C)    m/sec 
D)    m/sec

Question 7

The altitude (in feet) attained by a model rocket t sec into flight is given by the function   .
When is the rocket ascending, and when is it descending? What is the maximum altitude attained by the rocket?

Accepted Answer

The answer of The altitude (in feet) attained by a...

Question 8

Find a cubic function   that has a local maximum value of 112 at 1 and a local minimum value of -1,184 at 7.

Accepted Answer

The answer of Find a cubic function   that...

Question 9

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

Accepted Answer

The answer of Sketch the graph of the function ...

Question 10

What is the function of the graph?

Accepted Answer

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

Question 11

Use Newton's method to find the point of intersection of the graphs of   and   to within 0.00001 by solving the equation   using

Accepted Answer

The answer of Use Newton's method to find the point...

Question 12

Use Newton's method to approximate the zero of   between   and   using   . Continue until two successive approximations differ by less than 0.00001.

Accepted Answer

A) 0.16904 
B) 0.11154 
C) 0.23624 
D) 0.07984 
A) 0.16904 
B) 0.11154 
C) 0.23624 
D) 0.07984

Question 13

Find the critical numbers of the function.

Accepted Answer

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

Question 14

Use the graph of f to find the given limits.
(a)   (b)

Accepted Answer

The answer of Use the graph of f to find...

Question 15

What is the function of the graph?

Accepted Answer

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

Question 16

What constant acceleration is required to increase the speed of a car from 30 ft/s to 45 ft/s in
4 s?

Accepted Answer

The answer of What constant acceleration is required to increase...

Question 17

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

Accepted Answer

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

Question 18

Evaluate the limit.

Accepted Answer

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

Question 19

A woman at a point A on the shore of a circular lake with radius   wants to arrive at the point C diametrically opposite on the other side of the lake in the shortest possible time. She can walk at the rate of   and row a boat at   . How should she proceed? (Find   ). Round the result, if necessary, to the nearest hundredth.

Accepted Answer

A)    radians 
B) She should walk around the lake from point A to point C. 
C) She should row from point A to point C radians 
D)    radians 
E)    radians 
A)    radians 
B) She should walk around the lake from point A to point C. 
C) She should row from point A to point C radians 
D)    radians 
E)    radians

Question 20

Estimate the extreme values of the function.

Accepted Answer

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

Find the inflection points for the function given. ,

Sketch the curve.

Use Newton's method to approximate the indicated root of in the interval , correct to six decimal places. Use as the initial approximation.

Find the absolute maximum value of on the interval .

Find the maximum and minimum points of the function.

A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and before deploying her parachute is given by where is measured in meters per second. What is her terminal velocity? Hint: Evaluate

The altitude (in feet) attained by a model rocket t sec into flight is given by the function . When is the rocket ascending, and when is it descending? What is the maximum altitude attained by the rocket?

Find a cubic function that has a local maximum value of 112 at 1 and a local minimum value of -1,184 at 7.

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

What is the function of the graph?

Use Newton's method to find the point of intersection of the graphs of and to within 0.00001 by solving the equation using

Use Newton's method to approximate the zero of between and using . Continue until two successive approximations differ by less than 0.00001.

Find the critical numbers of the function.

Use the graph of f to find the given limits. (a) (b)

What is the function of the graph?

What constant acceleration is required to increase the speed of a car from 30 ft/s to 45 ft/s in 4 s?

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

Evaluate the limit.

Estimate the extreme values of the function.

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 the inflection points for the function given. ,

Sketch the curve.

Use Newton's method to approximate the indicated root of in the interval , correct to six decimal places. Use as the initial approximation.

Find the absolute maximum value of on the interval .

Find the maximum and minimum points of the function.

A skydiver leaps from a helicopter hovering high above the ground. Her velocity t sec later and before deploying her parachute is given by where is measured in meters per second. What is her terminal velocity? Hint: Evaluate

The altitude (in feet) attained by a model rocket t sec into flight is given by the function . When is the rocket ascending, and when is it descending? What is the maximum altitude attained by the rocket?

Find a cubic function that has a local maximum value of 112 at 1 and a local minimum value of -1,184 at 7.

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

What is the function of the graph?

Use Newton's method to find the point of intersection of the graphs of and to within 0.00001 by solving the equation using

Use Newton's method to approximate the zero of between and using . Continue until two successive approximations differ by less than 0.00001.

Find the critical numbers of the function.

Use the graph of f to find the given limits. (a) (b)

What is the function of the graph?

What constant acceleration is required to increase the speed of a car from 30 ft/s to 45 ft/s in 4 s?

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

Evaluate the limit.

Estimate the extreme values of the function.

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