Elementary Calculus

Question 1

What is the maximum or minimum point for the curve y = x2 − 4 ?

A. A minimum at (0, -4) B. A maximum at (0, -4)

C. A minimum at (0, 4) D. A maximum at (0, 4)

Question 2

What is the maximum or minimum point for the curve y = 4x − x4?

A. A minimum at (-1, -3) B. A maximum at (-1, -3)

C. A minimum at (1, 3) D. A maximum at (1, 3)

Question 3

What is the maximum or minimum point for the curve y = -3x2 − 12x + 5?

A. A minimum at (-2, 17) B. A maximum at (-2, 17)

C. A minimum at (2, -31) D. A maximum at (2, -31)

Question 4

A rectangle has length x m and its perimeter is 20 m What is the maximum area of such a rectangle?

A. 20 m2 B. 22.5 m2 C. 24 m2 D. 25 m2

Question 5

The diagram shows a square prism with cross-section x units by x units, and length (9 − 2x) units. What is the maximum volume of the prism?

A. 16 units3 B. 24 units3 C. 27 units3 D. 30 units3

Question 6

A ball is thrown in the air. Its height, h m, at any time t seconds is given by: h = 5t(4 − t). What is the maximum height reached by the ball?

A.20 m B.24 m C.25 m D.40 m

Question 7

What is the local maximum value of the function f(x) = x3 + 3x2 − 24x

A.-28 B.28 C.80 D.112

Question 8

What is the local minimum value of the function f(x) = x3(x + 4).

A. -189 B. -27 C. 27 D.12

Question 9

What is the local maximum value of the function f(x) = 2x3 − 24x − 32

A. -64 B. 0 C. 32 D. 96

Question 10

If 2x + y = 10, find the minimum value of x2 + y2.

A. 16 B. 20 C 21.25 D. 25