Mathematics

Mathematics

Problem

Let

g(x)=\int_{2}^{x} f(t)\,dt

, where

f

is continuous on an open interval

(a,b)

. Which of the following conditions on

f

is sufficient to conclude that

g

is decreasing on

(a,b)

? a)

f(x)>0

for every

x

in

(a,b)

b)

f(x)\le 0

for every

x

in

(a,b)

c)

f(x)<0

for every

x

in

(a,b)

d)

f(x)<0

for at least one

x

in

(a,b)

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