Part II: Specific Topics

Sample Multiple-Choice Questions:Applications 0' the Derivative

1. Find the x-coordinate of the absoluteminimum of f(x) = x3

_ x2- X + I on the

interval [-2, 2].

A. -2B. 1-3c. 0

D. IE. 2

2. The function f(x) = X 3 - 2x 2 isincreasing on which of the followinginterval( s)?

A. x < 0 only

B. x> 1onlyc. 0<x<1

D. x< 0 or x> 1E. 3x< 0 or x> 4"

3. Given f(x) =!x5- 214x4 find where the

relative extrema off"(x) occur.

A. 1x= 0, 12

.B. 1x=g

C. 1x= 24

D. 1x=O'g

E. Ix=O'6

1Q8

4. The position of a particle moving alonga horizontal line at any time t is given.by s (t) = 3t2

- 2t - 8. For what value(s)of t is the particle not moving?

A. t = 2 or t =-1B. t = 3 only

1C. t= 3"only

D. t = 1 or t = 4

E. t = 2 only

s. A particle moves in a straight line suchthat its distance at time t from a fixedpoint on the line is given by 8t - 3t 2units. What is the total distance coveredby the particle from t = 1 to t = 2?

A. 1 unit

B. 4 .3umts

c. 5 .3"umts

D. 2 units

E. 5 units

6. A particle moves along a horizontalpath such that its position at any timet is given by s (t) = (2t - 3)3~Thenumber of times the particle changesdirection is

A. 0B. 1

C. 2D. 3

E. not determinable from theinformation given