Mathematics

Mathematics

Problem

Let

f

be continuous on

\mathbb R

and define

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

. Suppose

f(x)>0

for

-2<x<1

and

f(x)<0

for

1<x<4

. Which statement about

F

is correct? a)

F

\, is increasing on

(-2,4)

b)

F

\, is increasing on

(-2,0)

and decreasing on

(0,1)

and

(1,4)

c)

F

\, is increasing on

(-2,1)

and decreasing on

(1,4)

d)

F

\, is decreasing on

(-2,1)

and increasing on

(1,4)

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