A continuous function satisfies for and for

MATHEMATICS · Subjective · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

A continuous function

f

satisfies

f(t)=2

for

0\le t<4

and

f(t)=-1

for

4\le t\le7

. Define the accumulation function

g(x)=\displaystyle \int_{0}^{x} f(t)\,dt

. Describe on which sub-intervals of

[0,7]

the function

g

is increasing and on which it is decreasing, and briefly explain your reasoning.