Question 1

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. 
A) x = -5/6. 
B) x = 3/5. 
C) x = -3/2. 
D) There is no critical point. A

Question 2

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) slope 
A) maximum. 
B) minimum. 
C) inflection point. 
D) slope C

Question 3

The slope of a straight line is constant when measured at any point along the line.

Accepted Answer

A) True 
 B)False  True

Question 4

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

Question 5

The derivative of a constant is one.

Accepted Answer

A) True 
 B)False

Question 6

The second derivative of the function 4   + 3   + 2   + x + 7 is 48   + 18x.

Accepted Answer

A) True 
 B)False

Question 7

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 8

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. 
A) 15x2 + 6x + 7. 
B) 6x2 + 7x + 9. 
C) 5x2 + 3x + 7. 
D) 3x2 + 2x + 7.

Question 9

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 10

The points of inflection of the curve     +   + x + 12 are X = 1 and X = -1.

Accepted Answer

A) True 
 B)False

Question 11

The second derivative of 8   + 7   + 3x + 9 is

Accepted Answer

A) 48   + 35
  +3. 
B) 960   + 420
  . 
C) 240   + 140
  . 
D) 320   + 120
  + 3
  + 9x. 
A) 48   + 35
  +3. 
B) 960   + 420
  . 
C) 240   + 140
  . 
D) 320   + 120
  + 3
  + 9x.

Question 12

The derivative of 2x2 + 2x + 7 is

Accepted Answer

A) 2x + 2. 
B) 1x + 7. 
C) 4x + 2. 
D) x2 + 7. 
A) 2x + 2. 
B) 1x + 7. 
C) 4x + 2. 
D) x2 + 7.

Question 13

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

Accepted Answer

A) True 
 B)False

Question 14

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 
A) 3 
B) 1 
C) 2 
D) 0

Question 15

The derivative of   is

Accepted Answer

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

Question 16

We can find a point of inflection by simply setting the second derivative of the nonlinear function equal to zero and solving.

Accepted Answer

A) True 
 B)False

Question 17

Find the slope of the line Y = 4X-3 at the point where X = 17.

Accepted Answer

The answer of Find the slope of the line Y...

Question 18

Through rigorous quantitative analysis, Geoff develops a trading algorithm that will permit him to gain a competitive advantage over his previous dartboard method of selecting stocks.What he has noticed is that a stock's value at the end of the month can be accurately forecast using the equation PriceEND =   + PriceSTART where PriceSTART is the stock price at the start of the month and x is the number of days until the next full moon.At what point in time will the stock be at its maximum and minimum? If SBUX is trading at $50 per share at the start of the month, what profit can Geoff realize if he buys 100 shares at its minimum price and sells all 100 shares at its maximum price.Assume Geoff pays a $10 fee for the buy order and another $10 for the sell order.

Accepted Answer

The first derivative is @#IMG-DLM& - 10x + 9 Infle

Question 19

What is the second derivative of 7   + 6   + 3   +9?

Accepted Answer

The answer of What is the second derivative of 7...

Question 20

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

Exam 21: Calculus-Based Optimization

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

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

The slope of a straight line is constant when measured at any point along the line.

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.

The derivative of a constant is one.

The second derivative of the function 4 + 3 + 2 + x + 7 is 48 + 18x.

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

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

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.

The points of inflection of the curve + + x + 12 are X = 1 and X = -1.

The second derivative of 8 + 7 + 3x + 9 is

The derivative of 2x2 + 2x + 7 is

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

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

The derivative of is

We can find a point of inflection by simply setting the second derivative of the nonlinear function equal to zero and solving.

Find the slope of the line Y = 4X-3 at the point where X = 17.

What is the second derivative of 7 + 6 + 3 +9?

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

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

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

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

The derivative of 2x² + 2x + 7 is

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