Question 1

Find the indicated derivative. Find   ​

Accepted Answer

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

Question 2

The sales of a product S (in thousands of dollars) are given by   , where x is the advertising expenditure (in thousands of dollars). Find the rate of change of sales with respect to advertising expenditure. Use the second derivative to find how this rate is changing at   . Round your answer to two decimal places. ​

Accepted Answer

A)  0.89 
B)  -0.03 
C)  0.00 
D)  -0.89 
E)  -0.02 
A)  0.89 
B)  -0.03 
C)  0.00 
D)  -0.89 
E)  -0.02

Question 3

Use properties of limits and algebraic methods to find the limit, if it exists. ​   ​

Accepted Answer

A)  0 
B)    
C)    
D)    
E)  does not exist 
A)  0 
B)    
C)    
D)    
E)  does not exist

Question 4

Differentiate the given function. ​   ​

Accepted Answer

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

Question 5

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​   ​

Accepted Answer

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

Question 6

Let   . Use the definition of derivative and the Procedure/Example table in this section to verify that   . Then, find the slope of the tangent to the graph of   at   . ​

Accepted Answer

A)  27 
B)  12 
C)  -27 
D)  -12 
E)  0 
A)  27 
B)  12 
C)  -27 
D)  -12 
E)  0

Question 7

Find   ​   ​

Accepted Answer

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

Question 8

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​   ​

Accepted Answer

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

Question 9

Determine whether the function is continuous or discontinuous at the given x-value. ​   ​

Accepted Answer

A)  discontinuous 
B)  continuous 
A)  discontinuous 
B)  continuous

Question 10

Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by   . Describe any discontinuities for C(p). Explain what each discontinuity means. ​

Accepted Answer

A)  C(p) is discontinuous at   . This means that not all pollution can be removed. 
B)  C(p) is discontinuous at   . This means that none of the pollution can be removed. 
C)  C(p) is continuous everywhere. 
D)  C(p) is discontinuous at   . This means that not all pollution can be removed. 
E)  C(p) is discontinuous at   . This means that none of the pollution can be removed. 
A)  C(p) is discontinuous at   . This means that not all pollution can be removed. 
B)  C(p) is discontinuous at   . This means that none of the pollution can be removed. 
C)  C(p) is continuous everywhere. 
D)  C(p) is discontinuous at   . This means that not all pollution can be removed. 
E)  C(p) is discontinuous at   . This means that none of the pollution can be removed.

Question 11

The tangent line to the graph of f (x) at   is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of f (x) at P. ​   ​

Accepted Answer

A)  -3 
B)  2 
C)  1 
D)  -4 
E)  does not exist 
A)  -3 
B)  2 
C)  1 
D)  -4 
E)  does not exist

Question 12

Suppose that for fiddler crabs, the allometric relationship between the weight C of the claw and the weight W of the body is given by   . Find the function that gives the rate of change of claw weight with respect to body weight. ​

Accepted Answer

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

Question 13

The data entry speed (in words per minute) of a data clerk trainee is   , where x is the number of hours of training he has had. What is the rate at which his speed is changing and what does this rate mean when he has had 15 hours of training? ​

Accepted Answer

A)  If the training hours are increased from 15 to 16 hours, the student's typing speed will increase about 5.00 words per minute. 
B)  If the training hours are increased from 15 to 16 hours, the student's typing speed will increase about 12.50 words per minute. 
C)  If the training hours are increased from 15 to 16 hours, the student's typing speed will increase about 6.25 words per minute. 
D)  If the training hours are increased from 15 to 16 hours, the student's typing speed will decrease about 5.00 words per minute. 
E)  If the training hours are increased from 15 to 16 hours, the student's typing speed will decrease about 2.18 words per minute. 
A)  If the training hours are increased from 15 to 16 hours, the student's typing speed will increase about 5.00 words per minute. 
B)  If the training hours are increased from 15 to 16 hours, the student's typing speed will increase about 12.50 words per minute. 
C)  If the training hours are increased from 15 to 16 hours, the student's typing speed will increase about 6.25 words per minute. 
D)  If the training hours are increased from 15 to 16 hours, the student's typing speed will decrease about 5.00 words per minute. 
E)  If the training hours are increased from 15 to 16 hours, the student's typing speed will decrease about 2.18 words per minute.

Question 14

For the function in this problem, approximate   by computing   with   . ​   ​

Accepted Answer

A)  72.9793 
B)  73.0369 
C)  73.0027 
D)  73.1261 
E)  72.8793 
A)  72.9793 
B)  73.0369 
C)  73.0027 
D)  73.1261 
E)  72.8793

Question 15

Use properties of limits and algebraic methods to find   if the limit exists. ​

Accepted Answer

A)  0 
B)  10 
C)  ∞ 
D)  -10 
E)  5 
A)  0 
B)  10 
C)  ∞ 
D)  -10 
E)  5

Question 16

Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit of the product according to   where p is in dollars. What is the rate of change in sales volume when the price is $20? Round your answer to three decimal places. ​

Accepted Answer

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

Question 17

Identify x-values where   ​   ​

Accepted Answer

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

Question 18

Differentiate the function   . ​

Accepted Answer

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

Question 19

Differentiate the given function. ​   ​

Accepted Answer

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

Question 20

When squares of side x inches are cut from the corners of a 35-inch-square piece of cardboard, an open-top box can be formed by folding up the sides. The volume of this box is given by   , find the rate of change of volume with respect to the size of the squares. ​

Accepted Answer

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

Find the indicated derivative. Find

Use properties of limits and algebraic methods to find the limit, if it exists.

Differentiate the given function.

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

Let . Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the slope of the tangent to the graph of at .

Find

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

Determine whether the function is continuous or discontinuous at the given x-value.

Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by . Describe any discontinuities for C(p). Explain what each discontinuity means.

The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of f (x) at P.

Suppose that for fiddler crabs, the allometric relationship between the weight C of the claw and the weight W of the body is given by . Find the function that gives the rate of change of claw weight with respect to body weight.

The data entry speed (in words per minute) of a data clerk trainee is , where x is the number of hours of training he has had. What is the rate at which his speed is changing and what does this rate mean when he has had 15 hours of training?

For the function in this problem, approximate by computing with .

Use properties of limits and algebraic methods to find if the limit exists.

Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit of the product according to where p is in dollars. What is the rate of change in sales volume when the price is $20? Round your answer to three decimal places.

Identify x-values where

Differentiate the function .

Differentiate the given function.

When squares of side x inches are cut from the corners of a 35-inch-square piece of cardboard, an open-top box can be formed by folding up the sides. The volume of this box is given by , find the rate of change of volume with respect to the size of the squares.

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 Continued

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

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Exam 9: Derivatives

Find the indicated derivative. Find ​

Use properties of limits and algebraic methods to find the limit, if it exists. ​ ​

Differentiate the given function. ​ ​

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​ ​

Let . Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the slope of the tangent to the graph of at . ​

Find ​ ​

Find the derivative of the given function. Simplify and express the answer using positive exponents only. ​ ​

Determine whether the function is continuous or discontinuous at the given x-value. ​ ​

Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by . Describe any discontinuities for C(p). Explain what each discontinuity means. ​

The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of f (x) at P. ​ ​

Suppose that for fiddler crabs, the allometric relationship between the weight C of the claw and the weight W of the body is given by . Find the function that gives the rate of change of claw weight with respect to body weight. ​

The data entry speed (in words per minute) of a data clerk trainee is , where x is the number of hours of training he has had. What is the rate at which his speed is changing and what does this rate mean when he has had 15 hours of training? ​

For the function in this problem, approximate by computing with . ​ ​

Use properties of limits and algebraic methods to find if the limit exists. ​

Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit of the product according to where p is in dollars. What is the rate of change in sales volume when the price is $20? Round your answer to three decimal places. ​

Identify x-values where ​ ​

Differentiate the function . ​

Differentiate the given function. ​ ​

When squares of side x inches are cut from the corners of a 35-inch-square piece of cardboard, an open-top box can be formed by folding up the sides. The volume of this box is given by , find the rate of change of volume with respect to the size of the squares. ​

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 Continued

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

Find the indicated derivative. Find

Use properties of limits and algebraic methods to find the limit, if it exists.

Differentiate the given function.

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

Let . Use the definition of derivative and the Procedure/Example table in this section to verify that . Then, find the slope of the tangent to the graph of at .

Find

Find the derivative of the given function. Simplify and express the answer using positive exponents only.

Determine whether the function is continuous or discontinuous at the given x-value.

Suppose that the cost C of removing p percent of the particulate pollution from the exhaust gases at an industrial site is given by . Describe any discontinuities for C(p). Explain what each discontinuity means.

The tangent line to the graph of f (x) at is shown. On the tangent line, P is the point of tangency and A is another point on the line. Find the instantaneous rate of change of f (x) at P.

Suppose that for fiddler crabs, the allometric relationship between the weight C of the claw and the weight W of the body is given by . Find the function that gives the rate of change of claw weight with respect to body weight.

The data entry speed (in words per minute) of a data clerk trainee is , where x is the number of hours of training he has had. What is the rate at which his speed is changing and what does this rate mean when he has had 15 hours of training?

For the function in this problem, approximate by computing with .

Use properties of limits and algebraic methods to find if the limit exists.

Suppose that the weekly sales volume y (in thousands of units sold) depends on the price per unit of the product according to where p is in dollars. What is the rate of change in sales volume when the price is $20? Round your answer to three decimal places.

Identify x-values where

Differentiate the function .

Differentiate the given function.

When squares of side x inches are cut from the corners of a 35-inch-square piece of cardboard, an open-top box can be formed by folding up the sides. The volume of this box is given by , find the rate of change of volume with respect to the size of the squares.