A differentiable function has derivative

MATHEMATICS · Multi-part · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

A differentiable function

g

has derivative

g'(x)=h(x)

, where

h

is described below. For

0 \le x \le 6

, the

x

-axis, the graph of

h

, and the line

x=6

bound two regions: • Region

R_1

(from

x=0

x=2

) is a rectangle of height

4

. • Region

R_2

(from

x=2

x=6

) is a right triangle whose base lies on the

x

-axis, vertex at

(2,4)

, and hypotenuse sloping down to the

x

-axis at

(6,0)

. Assume

h(x) \ge 0

[0,6]

and

g(0)=3

. Answer the following, showing all steps. (a) Compute

g(2)

. (b) Compute

g(6)

. (c) Determine the average (mean) value of

h

on the interval

[0,6]

and interpret its meaning in the context of

g

. Include units in your interpretation.