Let be continuous on for

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f

be continuous on

1<t<5

with

f(t)<0

for

1<t<3

and

f(t)>0

for

3<t<5

. Let

g(x)=\displaystyle\int_{1}^{x} f(t)\,dt

. Which statement about the behavior of

g

on the interval

1<x<5

is most accurate? (a)

g

is increasing on

(1,3)

and decreasing on

(3,5)

. (b)

g

is decreasing on both

(1,3)

and

(3,5)

. (c)

g

is decreasing on

(1,3)

and increasing on

(3,5)

. (d)

g

is increasing on both

(1,3)

and

(3,5)