Deck 21: Calculus-Based Optimization

Question 1

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

Answer 1

True

Question 2

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.

Answer 2

False

Question 3

The derivative of is

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

Answer 3

B

Question 4

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

Question 5

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

Question 6

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

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

Question 7

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

Question 8

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.

Question 9

The critical point for the function y = 7x² - 7x + 4 lies at

A)x = -1.
B)x = 1.
C)x = -1/2.
D)x = 1/2.
E)None of the above

Question 10

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

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

Question 11

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

Question 12

The derivative of a constant is one.

Question 13

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

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

Question 14

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

Question 15

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

Question 16

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

Question 17

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

Question 18

The derivative of 2x² + 2x + 7 is

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

Question 19

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

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

Question 20

The derivative of 19x⁴ + 2x³ + 5x² + 1x + 9 is

A)19x³ + 2x² + 5x + 1.
B)4x³ + 3x² + 2x + 1.
C)12x² + 6x + 9.
D)76x³ + 6x² + 10x + 1.
E)None of the above

Question 21

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?

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

Question 22

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

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

Question 23

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

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

Question 24

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

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