Question 1

Find a function with the given derivative.

Accepted Answer

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

Question 2

Prove that   has exactly two solutions.

Accepted Answer

Let @#IMG-DLM& . The function f (x) is continuous

Question 3

Find the location of all horizontal and vertical tangents for   .

Accepted Answer

A)  horizontal: none; vertical: (-4, 0), (4, 0) 
B)  horizontal: (4, 0); vertical: (-4, 0), (4, 0) 
C)  horizontal: (-4, 0), (4, 0); vertical: none 
D)  horizontal: none; vertical: (4, 0) 
A)  horizontal: none; vertical: (-4, 0), (4, 0) 
B)  horizontal: (4, 0); vertical: (-4, 0), (4, 0) 
C)  horizontal: (-4, 0), (4, 0); vertical: none 
D)  horizontal: none; vertical: (4, 0)

Question 4

Explain why it is not valid to use the Mean Value Theorem for the given function on the specified interval. Show that there is no value of c that makes the conclusion of the theorem true.   ,

Accepted Answer

The function is not continuous on the sp

Question 5

Find the derivative of   .

Accepted Answer

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

Question 6

Determine if the function   is increasing, decreasing, or neither.

Accepted Answer

A)  Increasing 
B)  Decreasing 
C)  Neither 
A)  Increasing 
B)  Decreasing 
C)  Neither

Question 7

Use the position function   feet to find the velocity at t = 3 seconds. (Round answer to 2 decimal places.)

Accepted Answer

A)  v(3) = -51.85 ft/s 
B)  v(3) = -56.15 ft/s 
C)  v(3) = 56.15 ft/s 
D)  v(3) = -57.38 ft/s 
A)  v(3) = -51.85 ft/s 
B)  v(3) = -56.15 ft/s 
C)  v(3) = 56.15 ft/s 
D)  v(3) = -57.38 ft/s

Question 8

Suppose a sprinter reaches the following distances in the given times. Estimate the velocity of the sprinter at the 6 second mark. Round to the nearest integer. t sec
5
5)5
6
6)5
7   ft
121)7
142)5
158)5
174)7
193)9

Accepted Answer

A)  32 ft/sec 
B)  36 ft/sec 
C)  26 ft/sec 
D)  28 ft/sec 
A)  32 ft/sec 
B)  36 ft/sec 
C)  26 ft/sec 
D)  28 ft/sec

Question 9

Find the equation of the tangent line to   at

Accepted Answer

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

Question 10

Find y′(x) implicitly.

Accepted Answer

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

Question 11

Find an equation of the line tangent to   at x = 2.

Accepted Answer

A)  y = -2x + 3 
B)  y = -2x 
C)  y = 2x + 3 
D)  y = -2x + 5 
A)  y = -2x + 3 
B)  y = -2x 
C)  y = 2x + 3 
D)  y = -2x + 5

Question 12

Find an equation of the line tangent to   at

Accepted Answer

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

Question 13

Using the position function   , find the velocity function.

Accepted Answer

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

Question 14

Given that   , find   .

Accepted Answer

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

Question 15

Prove that   has exactly one solution.

Accepted Answer

Let @#IMG-DLM& . The function f(x) is continuous a

Question 16

Find an equation of the tangent line at the given point.   at

Accepted Answer

The answer of Find an equation of the tangent line...

Question 17

Find an equation of the line tangent to   at x = -6.

Accepted Answer

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

Question 18

Below is a graph of   . Sketch a graph of   .

Accepted Answer

The answer of Below is a graph of  ...

Question 19

Find the second-degree polynomial (of the form ax2 + bx + c) such that f(0) = 0, f '(0) = 5, and f ''(0) = 1.

Accepted Answer

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

Question 20

Find the derivative where f is an unspecified differentiable function.

Accepted Answer

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

Find a function with the given derivative.

Prove that has exactly two solutions.

Find the location of all horizontal and vertical tangents for .

Explain why it is not valid to use the Mean Value Theorem for the given function on the specified interval. Show that there is no value of c that makes the conclusion of the theorem true. ,

Find the derivative of .

Determine if the function is increasing, decreasing, or neither.

Use the position function feet to find the velocity at t = 3 seconds. (Round answer to 2 decimal places.)

Suppose a sprinter reaches the following distances in the given times. Estimate the velocity of the sprinter at the 6 second mark. Round to the nearest integer. t sec 5 5)5 6 6)5 7 ft 121)7 142)5 158)5 174)7 193)9

Find the equation of the tangent line to at

Find y′(x) implicitly.

Find an equation of the line tangent to at x = 2.

Find an equation of the line tangent to at

Using the position function , find the velocity function.

Given that , find .

Prove that has exactly one solution.

Find an equation of the tangent line at the given point. at

Find an equation of the line tangent to at x = -6.

Below is a graph of . Sketch a graph of .

Find the second-degree polynomial (of the form ax² + bx + c) such that f(0) = 0, f '(0) = 5, and f ''(0) = 1.

Find the derivative where f is an unspecified differentiable function.

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 a function with the given derivative.

Prove that has exactly two solutions.

Find the location of all horizontal and vertical tangents for .

Explain why it is not valid to use the Mean Value Theorem for the given function on the specified interval. Show that there is no value of c that makes the conclusion of the theorem true. ,

Find the derivative of .

Determine if the function is increasing, decreasing, or neither.

Use the position function feet to find the velocity at t = 3 seconds. (Round answer to 2 decimal places.)

Suppose a sprinter reaches the following distances in the given times. Estimate the velocity of the sprinter at the 6 second mark. Round to the nearest integer. t sec 5 5)5 6 6)5 7 ft 121)7 142)5 158)5 174)7 193)9

Find the equation of the tangent line to at

Find y′(x) implicitly.

Find an equation of the line tangent to at x = 2.

Find an equation of the line tangent to at

Using the position function , find the velocity function.

Given that , find .

Prove that has exactly one solution.

Find an equation of the tangent line at the given point. at

Find an equation of the line tangent to at x = -6.

Below is a graph of . Sketch a graph of .

Find the second-degree polynomial (of the form ax2 + bx + c) such that f(0) = 0, f '(0) = 5, and f ''(0) = 1.

Find the derivative where f is an unspecified differentiable function.

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 second-degree polynomial (of the form ax² + bx + c) such that f(0) = 0, f '(0) = 5, and f ''(0) = 1.