Suppose is continuous on with for and for

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

Problem

Suppose

f

is continuous on

(0,6)

with

f(x)>0

for

0<x<3

and

f(x)<0

for

3<x<6

. Let

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

. Which of the following best describes the signs of

g'(2)

and

g'(4)

? (a)

g'(2)<0

and

g'(4)>0

(b)

g'(2)>0

and

g'(4)<0

(c)

g'(2)=0

and

g'(4)=0

(d)

g'(2)>0

and

g'(4)>0