Let be a continuous function such that for

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

Problem

Let

f

be a continuous function such that

f(x)>0

for

-2<x<1

and

3<x<6

f(x)<0

for

1<x<3

and

x>6

, and

f(x)=0

x=-2,1,3,6

. Define

F(x)=\int_{-2}^{x} f(t)\,dt

. Determine the

x

-value(s) where

F

attains a local maximum.