5 Steps to a 5 AP Calculus BC 2019

Areas, Volumes, and Arc Lengths 261

0

2

4

6

8

10

12

14

p(x)

y

x

12 34 56 7 8

Figure 12.1-5

TIP • Remember differentiability implies continuity, but the converse is not true, i.e.,
continuity does not imply differentiability, e.g., as in the case of a cusp or a corner.

Example 3

The position function of a moving particle on a coordinate axis is:

s=

∫t

0

f(x)dx, wheretis in seconds andsis in feet.

The functionfis a differentiable function and its graph is shown below in Figure 12.1-6.

–8

0

10

x

y

f(x)

12 3 4 5 6 7 8

(3,–5)

(4,–8)

Figure 12.1-6

(a) What is the particle’s velocity att=4?

(b) What is the particle’s position att=3?

(c) When is the acceleration zero?

(d) When is the particle moving to the right?

(e) Att=8, is the particle on the right side or left side of the origin?