Mathematics

Mathematics

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

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