Derivative Practice Family of f: f & f’ & f’’ Definition Of the Derivative Applied Derivatives NO Calc Applied Derivatives WITH Calc 100 100 100 100 100 200 200 200 200 200 300 300 300 300 300 400 400 400 400 400 500 500 500 500 500

(A) (B) (C) (D) (E)

Solution (100 pts) E.

If then is (A) (B) (C) (D) (E)

Solution (200 pts) A.

If then (A) 8 (B) 2 (C) -2 (D) -3 (E) -8

Solution (300 pts) C. -2

If what is the value of at (3, 4) (A) (B) (C) (D) (E)

Solution (400 pts) A.

Let f and g be differentiable functions with the following properties: I. for all x II. If and then (B) (C) (D) 0 (E) 2

Solution (500 pts) E. 2

(A) 1 (B) (C) (D) (E) If then

Solution (100 pts) E

The graph of the function changes concavity at x = (A) 3.29 (B) 2.21 (C) 1.34 (D) 0.41 (E) -0.39

Solution (200 pts) B 2.21

Let f be a function such that For all x in the closed interval [3,4] with selected values shown in the table. Which of the following must be true about X 3.2 3.3 3.4 3.5 f(x) 2.48 2.68 2.86 3.03 (A) (B) (C) (D) (E)

Solution (300 pts) D

is concave down for (A) (B) (C) (D) (E)

Solution (400 pts) E

What are all the values of x for which the function f defined by is increasing? There are no such values of x (B) (C) (D) (E) All values of x

Solution (500 pts) D.

Let For what value of x does (A) -2 (B) -1 (C) 1 (D) 2 (E) 4

Solution (100 pts) D 2

Let f be a function such that Which of the following must be true? f is continuous at x = 7 f is differentiable at x = 7 The derivative of f is continuous at x = 7 (A) I only (B) II only (C) I and II only (D) I and III only (E) II and III only

Solution (200 pts) C I and II only

(A) 0 (B) 1 (C) 30 (D) 300 (E) 3000

Solution (300 pts) D. 300

(A) 0 (B) 1/12 (C) 1/3 (D) 4/3 (E) nonexistent

Solution (400 pts) B. 1/12

(A) -1 (B) (C) (D) (E)

Solution (500 pts) B.

An equation of the line tangent to the graph of at is (A) (B) (C) (D) (E)

Solution (100 pts) C.

Let then (A) -1 (B) 0 (C) 1 (D) 2 (E) nonexistent

Solution (200 pts) A. -1

The minimum acceleration attained on the interval 0 ≤ t ≤ 4 by the particle whose velocity is given by is (A) -16 (B) -10 (C) -8 (D) -25/3 (E) -3

Solution (300 pts) D. -25/3

The maximum value of on the interval [0, 2] is (B) -7 (C) -2 (D) 0 (E) 2

Solution (400 pts) D. 0

A particle is moving on the x-axis with position given by Then the particle is at rest only when t = (A) (B) and (C) (D) (E)

Solution (500 pts) E.

Which of the following is an equation of the line tangent to the graph of at the point where (A) (B) (C) (D) (E)

Solution (100 pts) A.

The side of a cube is increasing at a constant rate of 0 The side of a cube is increasing at a constant rate of 0.2 centimeter per second. In terms of the surface area S, what is the rate of change of the volume of the cube, in cubic centimeters per second? (A) 0.1S (B) 0.2S (C) 0.6S (D) 0.04S (E) 0.008S

Solution (200 pts) A. 0.1S

which of the following must be true? Let f be a function that is differentiable on the open interval (-3, 7). If f(-1) = 4, f(2) = -5 and f(6) = 8, which of the following must be true? I. f has at least 2 zeroes II. f has a relative minimum at x = 2 III. For some c, 2 < c < 6, f(c) = 4 I only (B) II only (C) I and II only (D) I and III only (E) I, II, and III

Solution (300 pts) D. I and III only

f(x) = 6 has a solution in (2, 5) f’(x) = 6 has a solution in (2, 5) If f is continuous on [2, 5] and differentiable on (2, 5) with f(2) = -4 and f(5) = 14, which of the following statements must be true? f(x) = 6 has a solution in (2, 5) f’(x) = 6 has a solution in (2, 5) f’’(x) = 6 has a solution in (2, 5) (A) I only (B) II only (C) I and II only I and III only (E) I, II, and III

Solution (400 pts) C. I and II only

At the moment that a rectangle is 8 feet long and 3 feet wide, its length is increasing at 0.5 feet/minute and its width is decreasing at 1.5 feet/minute. The area is (A) decreasing at 10.5 square feet/minute (B) increasing at 13.5 square feet/minute (C) increasing at 8.5 square feet/minute (D) decreasing at 0.5 square feet/minute (E) decreasing at 0.75 square feet/minute

(A) decreasing at 10.5 square feet/minute Solution (500 pts) (A) decreasing at 10.5 square feet/minute