Question 1

The second derivative tells about the slope of the first derivative.

Accepted Answer

A) True 
 B)False  True

Question 2

The second derivative of 7x4 + 6x3 + 5x + 3 is

Accepted Answer

A) 7x3 + 6x2 + 5. 
B) 28x3 + 18x2 + 5x + 3. 
C) 28x3 + 18x2 + 5. 
D) 84x2 + 36x. 
E) None of the above 
A) 7x3 + 6x2 + 5. 
B) 28x3 + 18x2 + 5x + 3. 
C) 28x3 + 18x2 + 5. 
D) 84x2 + 36x. 
E) None of the above D

Question 3

The derivative of   is

Accepted Answer

A)    
B) -   
C)    
D)    
E) None of the above 
A)    
B) -   
C)    
D)    
E) None of the above B

Question 4

Find the point at which the following function is a maximum:   - 2x2 + 3x + 6.

Accepted Answer

A) x = 3 
B) x = 1 
C) x = 0 
D) x = -3 
E) None of the above 
A) x = 3 
B) x = 1 
C) x = 0 
D) x = -3 
E) None of the above

Question 5

Find the point at which the following function is a minimum: y =   - 2x2 + 3x + 6.

Accepted Answer

A) x = 3 
B) x = 1 
C) x = 0 
D) x = -3 
E) None of the above 
A) x = 3 
B) x = 1 
C) x = 0 
D) x = -3 
E) None of the above

Question 6

The derivative of 2x2 + 2x + 7 is

Accepted Answer

A) 2x + 2. 
B) 1x + 7. 
C) 4x + 2. 
D) x2 + 7. 
E) None of the above 
A) 2x + 2. 
B) 1x + 7. 
C) 4x + 2. 
D) x2 + 7. 
E) None of the above

Question 7

Find the point at which the following function has an inflection point: y =   - 2x2 + 3x + 6.

Accepted Answer

A) 3 
B) 1 
C) 2 
D) 0 
E) None of the above 
A) 3 
B) 1 
C) 2 
D) 0 
E) None of the above

Question 8

To maximize total revenues,one can set the derivative of the total revenue function equal to zero and solve.

Accepted Answer

A) True 
 B)False

Question 9

The EOQ model is obtained by taking the second derivative of the revenue function.

Accepted Answer

A) True 
 B)False

Question 10

The derivative of 5x3 + 3x2 + 7x + 9 is

Accepted Answer

A) 15X2 + 6x + 7. 
B) 6x2 + 7x + 9. 
C) 5x2 + 3x + 7. 
D) 3x2 + 2x + 7. 
E) None of the above 
A) 15X2 + 6x + 7. 
B) 6x2 + 7x + 9. 
C) 5x2 + 3x + 7. 
D) 3x2 + 2x + 7. 
E) None of the above

Question 11

The slope of a nonlinear function varies depending on the point along the line at which it is measured.

Accepted Answer

A) True 
 B)False

Question 12

Profit for the Dew Drop Inn Country Diner is given by p = -0.1q2 + 1.80q + 100,where p is profit and q is the number of customers.What number of customers maximizes profit?

Accepted Answer

A) 100 
B) 900 
C) 300 
D) 9 
E) None of the above 
A) 100 
B) 900 
C) 300 
D) 9 
E) None of the above

Question 13

Find the critical point for the function y = X3 + 60.This point is a(n)

Accepted Answer

A) maximum. 
B) minimum. 
C) inflection point. 
D) Could be any of the above 
E) None of the above 
A) maximum. 
B) minimum. 
C) inflection point. 
D) Could be any of the above 
E) None of the above

Question 14

The critical point for the function y = 3x2 + 5x + 2 is at

Accepted Answer

A) x = -5/6. 
B) x = 3/5. 
C) x = -3/2. 
D) There is no critical point 
E) None of the above 
A) x = -5/6. 
B) x = 3/5. 
C) x = -3/2. 
D) There is no critical point 
E) None of the above

Question 15

To determine the slope of a nonlinear function at a point,we must find the slope of a line tangent to the point.

Accepted Answer

A) True 
 B)False

Question 16

The derivative of a constant is one.

Accepted Answer

A) True 
 B)False

Question 17

If,for a nonlinear function,the first derivative is equal to zero and the second derivative is equal to zero,we have both a maximum and a minimum occurring simultaneously.

Accepted Answer

A) True 
 B)False

Question 18

A zero value for the derivative of a nonlinear function always indicates the location of a maximum or minimum.

Accepted Answer

A) True 
 B)False

Question 19

At a minimum of a nonlinear function,the first derivative is equal to zero,and the second derivative is positive.

Accepted Answer

A) True 
 B)False

Question 20

The first step in attempting to find a minimum or maximum of a nonlinear function is to take the derivative of the function,set it equal to zero,and solve for x.

Accepted Answer

A) True 
 B)False

Exam 21: Calculus-Based Optimization

The second derivative tells about the slope of the first derivative.

The second derivative of 7x4 + 6x3 + 5x + 3 is

The derivative of is

Find the point at which the following function is a maximum: - 2x2 + 3x + 6.

Find the point at which the following function is a minimum: y = - 2x2 + 3x + 6.

The derivative of 2x2 + 2x + 7 is

Find the point at which the following function has an inflection point: y = - 2x2 + 3x + 6.

To maximize total revenues,one can set the derivative of the total revenue function equal to zero and solve.

The EOQ model is obtained by taking the second derivative of the revenue function.

The derivative of 5x3 + 3x2 + 7x + 9 is

The slope of a nonlinear function varies depending on the point along the line at which it is measured.

Profit for the Dew Drop Inn Country Diner is given by p = -0.1q2 + 1.80q + 100,where p is profit and q is the number of customers.What number of customers maximizes profit?

Find the critical point for the function y = X3 + 60.This point is a(n)

The critical point for the function y = 3x2 + 5x + 2 is at

To determine the slope of a nonlinear function at a point,we must find the slope of a line tangent to the point.

The derivative of a constant is one.

If,for a nonlinear function,the first derivative is equal to zero and the second derivative is equal to zero,we have both a maximum and a minimum occurring simultaneously.

A zero value for the derivative of a nonlinear function always indicates the location of a maximum or minimum.

At a minimum of a nonlinear function,the first derivative is equal to zero,and the second derivative is positive.

The first step in attempting to find a minimum or maximum of a nonlinear function is to take the derivative of the function,set it equal to zero,and solve for x.

Introduction to Quantitative Analysis

Probability Concepts and Applications

Decision Analysis

Regression Models

Forecasting

Inventory Control Models

Linear Programming Models: Graphical and Computer Methods

Linear Programming Applications

Transportation,assignment,and Network Models

Integer Programming,goal Programming,and Nonlinear Programming

Project Management

Waiting Lines and Queuing Theory Models

Simulation Modeling

Markov Analysis

Statistical Quality Control

Analytic Hierarchy Process

Dynamic Programming

Decision Theory and the Normal Distribution

Game Theory

Mathematical Tools: Determinants and Matrices

Linear Programming: The Simplex Method

Transportation, Assignment, and Network Algorithms

Filters

The second derivative of 7x⁴ + 6x³ + 5x + 3 is

Find the point at which the following function is a maximum: - 2x² + 3x + 6.

Find the point at which the following function is a minimum: y = - 2x² + 3x + 6.

The derivative of 2x² + 2x + 7 is

Find the point at which the following function has an inflection point: y = - 2x² + 3x + 6.

The derivative of 5x³ + 3x² + 7x + 9 is

Profit for the Dew Drop Inn Country Diner is given by p = -0.1q₂+ 1.80q + 100,where p is profit and q is the number of customers.What number of customers maximizes profit?

Find the critical point for the function y = X³ + 60.This point is a(n)

The critical point for the function y = 3x² + 5x + 2 is at