Mathematics

Mathematics

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)

.

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