Question 1

Find the derivative of f(x) = -5x2 + 2x - 5.

Accepted Answer

A)  -5x + 2 
B)  -10x2 - 5 
C)  -10x + 2 
D)  10x - 2 
A)  -5x + 2 
B)  -10x2 - 5 
C)  -10x + 2 
D)  10x - 2

Question 2

Find the average velocity for an object between t = 2 sec and t = 2.1 sec if f(t) = -16t2 + 100t + 10 represents its position in feet.

Accepted Answer

A)  34.4 ft/s 
B)  36 ft/s 
C)  32.8 ft/s 
D)  146 ft/s 
A)  34.4 ft/s 
B)  36 ft/s 
C)  32.8 ft/s 
D)  146 ft/s

Question 3

Find the derivative of   .

Accepted Answer

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

Question 4

Determine if the function satisfies Rolle's Theorem on the given interval. If so, find all values of c that make the conclusion of the theorem true.

Accepted Answer

A)    
B)    
C)      
D)  Rolle's Theorem not satisfied 
A)    
B)    
C)      
D)  Rolle's Theorem not satisfied

Question 5

Find the derivative   implicitly if   .

Accepted Answer

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

Question 6

The height of an object at time t is given by   . Determine the object's velocity at t = 4.

Accepted Answer

A)  130 
B)  -136 
C)  -130 
D)  -66 
A)  130 
B)  -136 
C)  -130 
D)  -66

Question 7

Compute the slope of the secant line between the points x = 2.9 and x = 3. Round your answer to the thousandths place.

Accepted Answer

A)  -0.981 
B)  1.852 
C)  -4.372 
D)  -1.963 
A)  -0.981 
B)  1.852 
C)  -4.372 
D)  -1.963

Question 8

Find an equation of the line tangent to   at   if   ,   ,   , and   .

Accepted Answer

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

Question 9

The total charge in an electrical circuit is given by   . The current is the rate of change of the charge,   . Determine the current at   (Round answer to 2 decimal places.)

Accepted Answer

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

Question 10

Find the derivative   implicitly.

Accepted Answer

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

Question 11

List the points A, B, C, D, and E in order of increasing slope of the tangent line.

Accepted Answer

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

Question 12

Find an equation of the tangent line to y = f(x) at x = -3.

Accepted Answer

A)  y = -6x + 18 
B)  y = 22x - 45 
C)  y = 6x + 18 
D)  y = 22x + 45 
A)  y = -6x + 18 
B)  y = 22x - 45 
C)  y = 6x + 18 
D)  y = 22x + 45

Question 13

Differentiate the function.

Accepted Answer

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

Question 14

Find all functions g such that

Accepted Answer

A)    
B)    
C)    for some constant C 
D)    for some constant C 
A)    
B)    
C)    for some constant C 
D)    for some constant C

Question 15

Find the equation of the tangent line to   at

Accepted Answer

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

Question 16

Differentiate the function.

Accepted Answer

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

Question 17

Compute the right-hand derivative   and the left-hand derivative   .

Accepted Answer

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

Question 18

Differentiate the function.

Accepted Answer

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

Question 19

Find the derivative of   .

Accepted Answer

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

Question 20

Use the position function   meters to find the velocity at t = 2 seconds. (Round answer to 2 decimal places.)

Accepted Answer

A)  v(2) = -19.79 m/s 
B)  v(2) = 8.32 m/s 
C)  v(2) = 0.73 m/s 
D)  v(2) = 2.91 m/s 
A)  v(2) = -19.79 m/s 
B)  v(2) = 8.32 m/s 
C)  v(2) = 0.73 m/s 
D)  v(2) = 2.91 m/s

Find the derivative of f(x) = -5x² + 2x - 5.

Find the average velocity for an object between t = 2 sec and t = 2.1 sec if f(t) = -16t² + 100t + 10 represents its position in feet.

Find the derivative of .

Determine if the function satisfies Rolle's Theorem on the given interval. If so, find all values of c that make the conclusion of the theorem true.

Find the derivative implicitly if .

The height of an object at time t is given by . Determine the object's velocity at t = 4.

Compute the slope of the secant line between the points x = 2.9 and x = 3. Round your answer to the thousandths place.

Find an equation of the line tangent to at if , , , and .

The total charge in an electrical circuit is given by . The current is the rate of change of the charge, . Determine the current at (Round answer to 2 decimal places.)

Find the derivative implicitly.

List the points A, B, C, D, and E in order of increasing slope of the tangent line.

Find an equation of the tangent line to y = f(x) at x = -3.

Differentiate the function.

Find all functions g such that

Find the equation of the tangent line to at

Differentiate the function.

Compute the right-hand derivative and the left-hand derivative .

Differentiate the function.

Find the derivative of .

Use the position function meters to find the velocity at t = 2 seconds. (Round answer to 2 decimal places.)

Preliminaries

Limits and Continuity

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 3: Differentiation

Find the derivative of f(x) = -5x2 + 2x - 5.

Find the average velocity for an object between t = 2 sec and t = 2.1 sec if f(t) = -16t2 + 100t + 10 represents its position in feet.

Find the derivative of .

Determine if the function satisfies Rolle's Theorem on the given interval. If so, find all values of c that make the conclusion of the theorem true.

Find the derivative implicitly if .

The height of an object at time t is given by . Determine the object's velocity at t = 4.

Compute the slope of the secant line between the points x = 2.9 and x = 3. Round your answer to the thousandths place.

Find an equation of the line tangent to at if , , , and .

The total charge in an electrical circuit is given by . The current is the rate of change of the charge, . Determine the current at (Round answer to 2 decimal places.)

Find the derivative implicitly.

List the points A, B, C, D, and E in order of increasing slope of the tangent line.

Find an equation of the tangent line to y = f(x) at x = -3.

Differentiate the function.

Find all functions g such that

Find the equation of the tangent line to at

Differentiate the function.

Compute the right-hand derivative and the left-hand derivative .

Differentiate the function.

Find the derivative of .

Use the position function meters to find the velocity at t = 2 seconds. (Round answer to 2 decimal places.)

Preliminaries

Limits and Continuity

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Find the derivative of f(x) = -5x² + 2x - 5.

Find the average velocity for an object between t = 2 sec and t = 2.1 sec if f(t) = -16t² + 100t + 10 represents its position in feet.