Mathematics

Mathematics

Problem

A continuous function

f

satisfies

f(t)>0

for

0<t<3

,

f(3)=0

, and

f(t)<0

for

3<t<8

. Let

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

. Which statement about

F

on the interval

(0,8)

is true? a)

F

is decreasing on

(0,3)

and increasing on

(3,8)

. b)

F

is increasing on

(0,3)

and on

(3,8)

. c)

F

is increasing on

(0,3)

and decreasing on

(3,8)

. d)

F

is decreasing on

(0,3)

and on

(3,8)

.

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