Question 1

For the given equation, find the slope of the tangent to the curve at the point   . Round your answer to two decimal places. ​   ​

Accepted Answer

A) -7.10 
B) 7.10 
C) -1.10 
D) -2.00 
E) undefined 
A) -7.10 
B) 7.10 
C) -1.10 
D) -2.00 
E) undefined E

Question 2

At what   -value does the curve defined by   have a vertical tangent? ​

Accepted Answer

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

Question 3

If   , find   .

Accepted Answer

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

Question 4

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 5

Assume that s, r, and h are differentiable functions of t. If   , find   when   ,   ,   , and   . Round your answer to two decimal places.

Accepted Answer

A) 0.36 
B) 1.50 
C) 0.50 
D) 2.63 
E) 0.93 
A) 0.36 
B) 1.50 
C) 0.50 
D) 2.63 
E) 0.93

Question 6

Assume that x and y are differentiable functions of t. Find   using the given values. Round your answer to two decimal places. ​   for   .
​

Accepted Answer

A) 0.22 
B) 0.67 
C) -0.67 
D) -0.22 
A) 0.22 
B) 0.67 
C) -0.67 
D) -0.22

Question 7

Find the y-value at the relative minima, and use a graphing utility to check your result. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E) does not exist 
A)    
B)    
C)    
D)    
E) does not exist

Question 8

Suppose that the revenue in dollars from the sale of x units of a product is given by   . Find the marginal revenue function. ​

Accepted Answer

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

Question 9

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 10

For the given equation, find the slope of the tangent to the curve at the point   . Round your answer to two decimal places. ​   ​

Accepted Answer

A) 0.00 
B) -11.06 
C) 11.24 
D) -85.06 
E) -84.54 
A) 0.00 
B) -11.06 
C) 11.24 
D) -85.06 
E) -84.54

Question 11

Assume that x and y are differentiable functions of t. In each case, find   given that   ,   , and   . ​   ​

Accepted Answer

A) 11 
B) 13 
C) 22 
D) 1 
E) -22 
A) 11 
B) 13 
C) 22 
D) 1 
E) -22

Question 12

The demand functions for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the interval in which the demand is elastic. Round your answer to two decimal places. ​   ​

Accepted Answer

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

Question 13

The demand functions for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the interval in which the demand is inelastic. Round your answer to two decimal places. ​   ​

Accepted Answer

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

Question 14

Find   . ​   ​

Accepted Answer

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

Question 15

The sales decay for a product is given by   , where S is the daily sales in dollars and t is the number of days since the end of a promotional campaign. Find the rate of change of sales decay. ​

Accepted Answer

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

Question 16

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 17

Find the derivative of the following function.

Accepted Answer

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

Question 18

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 19

Find dy/dx for the following equation: ​   .
​

Accepted Answer

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

Question 20

Find the derivative of the following function. ​
​   ​

Accepted Answer

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

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places.

At what -value does the curve defined by have a vertical tangent?

If , find .

Find the derivative of the following function.

Assume that s, r, and h are differentiable functions of t. If , find when , , , and . Round your answer to two decimal places.

Assume that x and y are differentiable functions of t. Find using the given values. Round your answer to two decimal places. for .

Find the y-value at the relative minima, and use a graphing utility to check your result.

Suppose that the revenue in dollars from the sale of x units of a product is given by . Find the marginal revenue function.

Find the derivative of the following function.

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places.

Assume that x and y are differentiable functions of t. In each case, find given that , , and .

The demand functions for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the interval in which the demand is elastic. Round your answer to two decimal places.

The demand functions for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the interval in which the demand is inelastic. Round your answer to two decimal places.

Find .

The sales decay for a product is given by , where S is the daily sales in dollars and t is the number of days since the end of a promotional campaign. Find the rate of change of sales decay.

Find the derivative of the following function.

Find the derivative of the following function.

Find the derivative of the following function.

Find dy/dx for the following equation: .

Find the derivative of the following function.

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

Exam 12: Derivatives Continued

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places. ​ ​

At what -value does the curve defined by have a vertical tangent? ​

If , find .

Find the derivative of the following function. ​ ​

Assume that s, r, and h are differentiable functions of t. If , find when , , , and . Round your answer to two decimal places.

Assume that x and y are differentiable functions of t. Find using the given values. Round your answer to two decimal places. ​ for . ​

Find the y-value at the relative minima, and use a graphing utility to check your result. ​ ​

Suppose that the revenue in dollars from the sale of x units of a product is given by . Find the marginal revenue function. ​

Find the derivative of the following function. ​ ​

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places. ​ ​

Assume that x and y are differentiable functions of t. In each case, find given that , , and . ​ ​

The demand functions for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the interval in which the demand is elastic. Round your answer to two decimal places. ​ ​

The demand functions for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the interval in which the demand is inelastic. Round your answer to two decimal places. ​ ​

Find . ​ ​

The sales decay for a product is given by , where S is the daily sales in dollars and t is the number of days since the end of a promotional campaign. Find the rate of change of sales decay. ​

Find the derivative of the following function. ​ ​

Find the derivative of the following function.

Find the derivative of the following function. ​ ​

Find dy/dx for the following equation: ​ . ​

Find the derivative of the following function. ​ ​ ​

Algebraic Concepts

Linear Equations and Functions

Quadratic and Other Special Functions

Matrices

Inequalities and Linear Programming

Exponential and Logarithmic Functions

Mathematics of Finance

Introduction to Probability

Further Topics in Probability; Data Description

Derivatives

Applications of Derivatives

Indefinite Integrals

Definite Integrals: Techniques of Integration

Functions of Two or More Variables

Filters

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places.

At what -value does the curve defined by have a vertical tangent?

Find the derivative of the following function.

Assume that x and y are differentiable functions of t. Find using the given values. Round your answer to two decimal places. for .

Find the y-value at the relative minima, and use a graphing utility to check your result.

Suppose that the revenue in dollars from the sale of x units of a product is given by . Find the marginal revenue function.

Find the derivative of the following function.

For the given equation, find the slope of the tangent to the curve at the point . Round your answer to two decimal places.

Assume that x and y are differentiable functions of t. In each case, find given that , , and .

The demand functions for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the interval in which the demand is elastic. Round your answer to two decimal places.

The demand functions for specialty steel products are given, where p is in dollars and q is the number of units demanded. Find the interval in which the demand is inelastic. Round your answer to two decimal places.

Find .

The sales decay for a product is given by , where S is the daily sales in dollars and t is the number of days since the end of a promotional campaign. Find the rate of change of sales decay.

Find the derivative of the following function.

Find the derivative of the following function.

Find dy/dx for the following equation: .

Find the derivative of the following function.