Module 6 Calculus-Based Optimization

A) 2x + 2.

B) 1x + 7.

C) 4x + 2.

D) x2 + 7.

E) None of the above

14) 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

15) 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

16) The derivative of is

A)

B) -

C)

D)

E) None of the above

17) 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

18) 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

19) 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

20) 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

21) 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

22) 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

23) 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

24) 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