Question 1

Write the equation of the line tangent to the curve   at the point   .

Accepted Answer

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

Question 2

If the demand function for q units of a commodity at p$ per unit is given by   , find the rate of change of quantity with respect to price when p = $20. Round your answer to three decimal places. ​

Accepted Answer

A)  0.208 
B)  -0.208 
C)  0.104 
D)  -0.090 
E)  0.045 
A)  0.208 
B)  -0.208 
C)  0.104 
D)  -0.090 
E)  0.045

Question 3

Boyle's law for enclosed gases states that at a constant temperature, the pressure is related to the volume by the equation   , where k is a constant. If the volume is increasing at a rate of 2 cubic inches per hour, at what rate is the pressure changing when the volume is 50 cubic inches and k = 9 inch-pounds? Round your answer to three decimal places. ​

Accepted Answer

A)  0.025 lb/in2/hr 
B)  -0.004 lb/in2/hr 
C)  -1.235 lb/in2/hr 
D)  0.007 lb/in2/hr 
E)  -0.007 lb/in2/hr 
A)  0.025 lb/in2/hr 
B)  -0.004 lb/in2/hr 
C)  -1.235 lb/in2/hr 
D)  0.007 lb/in2/hr 
E)  -0.007 lb/in2/hr

Question 4

Suppose the weekly demand for a product is given by   and the weekly supply before taxation is given by   . Find the tax per item that produces maximum tax revenue. Round your answer to the nearest cent. ​

Accepted Answer

A)  $146.25 tax per item 
B)  $132.05 tax per item 
C)  $124.80 tax per item 
D)  $139.20 tax per item 
E)  $117.45 tax per item 
A)  $146.25 tax per item 
B)  $132.05 tax per item 
C)  $124.80 tax per item 
D)  $139.20 tax per item 
E)  $117.45 tax per item

Question 5

The lengths of the edges of a cube are increasing at a rate of 7 ft/min. At what rate is the surface area changing when the edges are 11 ft long? ​

Accepted Answer

A)  588 ft2/min 
B)  924 ft2/min 
C)  1,452 ft2/min 
D)  294 ft2/min 
E)  3,234 ft2/min 
A)  588 ft2/min 
B)  924 ft2/min 
C)  1,452 ft2/min 
D)  294 ft2/min 
E)  3,234 ft2/min

Question 6

Find   if   ​

Accepted Answer

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

Question 7

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 8

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Find   . ​   ​

Accepted Answer

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

Question 11

p is the price per unit in dollars and q is the number of units. If the daily demand for a product is given by the function   and the daily supply before taxation is   , find the tax per item that maximizes tax revenue. Round your answer to the nearest cent. ​

Accepted Answer

A)  $714.08 per item 
B)  $572.85 per item 
C)  $855.30 per item 
D)  $622.63 per item 
E)  $504.10 per item 
A)  $714.08 per item 
B)  $572.85 per item 
C)  $855.30 per item 
D)  $622.63 per item 
E)  $504.10 per item

Question 12

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 13

Assume that x and y are differentiable functions of t. Find   using the given values. ​   for   .
​

Accepted Answer

A)  102 
B)  78 
C)  128 
D)  126 
E)  62 
A)  102 
B)  78 
C)  128 
D)  126 
E)  62

Question 14

Find the derivative of the following function. ​   ​

Accepted Answer

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

Question 15

Write the equation of the line tangent to the curve   at the point   . ​

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   . ​   ​

Accepted Answer

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

Question 18

Find dy/dx at the given point without first solving for y. Round your answer to two decimal places.   at   ​

Accepted Answer

A)  -0.80 
B)  -0.30 
C)  1.45 
D)  0.15 
E)  0.45 
A)  -0.80 
B)  -0.30 
C)  1.45 
D)  0.15 
E)  0.45

Question 19

The demand function for a product is given by   , where p is the price per unit in dollars when x units are demanded. Find the second derivative to see whether the rate at which the price is changing at 30 units is increasing or decreasing. ​

Accepted Answer

A)  increasing 
B)  decreasing 
A)  increasing 
B)  decreasing

Question 20

p is the price per unit in dollars and q is the number of units. If the demand and supply functions for a product are   and   , respectively, find the tax per unit t that will maximize the tax revenue T. Round your answer to the nearest cent.

Accepted Answer

A)  $406.10 per item 
B)  $393.90 per item 
C)  $407.50 per item 
D)  $387.19 per item 
E)  $400.00 per item 
A)  $406.10 per item 
B)  $393.90 per item 
C)  $407.50 per item 
D)  $387.19 per item 
E)  $400.00 per item

Write the equation of the line tangent to the curve at the point .

If the demand function for q units of a commodity at p$ per unit is given by , find the rate of change of quantity with respect to price when p = $20. Round your answer to three decimal places.

Suppose the weekly demand for a product is given by and the weekly supply before taxation is given by . Find the tax per item that produces maximum tax revenue. Round your answer to the nearest cent.

The lengths of the edges of a cube are increasing at a rate of 7 ft/min. At what rate is the surface area changing when the edges are 11 ft long?

Find if

Find the derivative of the following function.

Find the derivative of the following function.

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

Find .

p is the price per unit in dollars and q is the number of units. If the daily demand for a product is given by the function and the daily supply before taxation is , find the tax per item that maximizes tax revenue. Round your answer to the nearest cent.

Find the derivative of the following function.

Assume that x and y are differentiable functions of t. Find using the given values. for .

Find the derivative of the following function.

Write the equation of the line tangent to the curve at the point .

Find the derivative of the following function.

Find .

Find dy/dx at the given point without first solving for y. Round your answer to two decimal places. at

The demand function for a product is given by , where p is the price per unit in dollars when x units are demanded. Find the second derivative to see whether the rate at which the price is changing at 30 units is increasing or decreasing.

p is the price per unit in dollars and q is the number of units. If the demand and supply functions for a product are and , respectively, find the tax per unit t that will maximize the tax revenue T. Round your answer to the nearest cent.

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 and Data Description

Derivatives

Derivatives

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

Exam 11: Derivatives Continued

Write the equation of the line tangent to the curve at the point .

If the demand function for q units of a commodity at p$ per unit is given by , find the rate of change of quantity with respect to price when p = $20. Round your answer to three decimal places. ​

Suppose the weekly demand for a product is given by and the weekly supply before taxation is given by . Find the tax per item that produces maximum tax revenue. Round your answer to the nearest cent. ​

The lengths of the edges of a cube are increasing at a rate of 7 ft/min. At what rate is the surface area changing when the edges are 11 ft long? ​

Find if ​

Find the derivative of the following function. ​ ​

Find the derivative of the following function. ​ ​

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

Find . ​ ​

p is the price per unit in dollars and q is the number of units. If the daily demand for a product is given by the function and the daily supply before taxation is , find the tax per item that maximizes tax revenue. Round your answer to the nearest cent. ​

Find the derivative of the following function. ​ ​

Assume that x and y are differentiable functions of t. Find using the given values. ​ for . ​

Find the derivative of the following function. ​ ​

Write the equation of the line tangent to the curve at the point . ​

Find the derivative of the following function. ​ ​

Find . ​ ​

Find dy/dx at the given point without first solving for y. Round your answer to two decimal places. at ​

The demand function for a product is given by , where p is the price per unit in dollars when x units are demanded. Find the second derivative to see whether the rate at which the price is changing at 30 units is increasing or decreasing. ​

p is the price per unit in dollars and q is the number of units. If the demand and supply functions for a product are and , respectively, find the tax per unit t that will maximize the tax revenue T. Round your answer to the nearest cent.

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 and Data Description

Derivatives

Derivatives

Indefinite Integrals

Definite Integrals - Techniques

A: Definite Integrals - Techniques

Functions of Two or More Variables

Algebraic Concepts 2

Algebraic Concepts 3

Algebraic Concepts 4

Algebraic Concepts 5

Filters

If the demand function for q units of a commodity at p$ per unit is given by , find the rate of change of quantity with respect to price when p = $20. Round your answer to three decimal places.

Suppose the weekly demand for a product is given by and the weekly supply before taxation is given by . Find the tax per item that produces maximum tax revenue. Round your answer to the nearest cent.

The lengths of the edges of a cube are increasing at a rate of 7 ft/min. At what rate is the surface area changing when the edges are 11 ft long?

Find if

Find the derivative of the following function.

Find the derivative of the following function.

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

Find .

p is the price per unit in dollars and q is the number of units. If the daily demand for a product is given by the function and the daily supply before taxation is , find the tax per item that maximizes tax revenue. Round your answer to the nearest cent.

Find the derivative of the following function.

Assume that x and y are differentiable functions of t. Find using the given values. for .

Find the derivative of the following function.

Write the equation of the line tangent to the curve at the point .

Find the derivative of the following function.

Find .

Find dy/dx at the given point without first solving for y. Round your answer to two decimal places. at

The demand function for a product is given by , where p is the price per unit in dollars when x units are demanded. Find the second derivative to see whether the rate at which the price is changing at 30 units is increasing or decreasing.