Let , where is continuous on an open interval . Which of the following conditions on…

MATHEMATICS · Single correct · AP · Calculus AB · Integration and Accumulation of Change · Integration and Accumulation of Change

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

(a,b)

(b)

f(x)\le 0

for every

x

(a,b)

(c)

f(x)<0

for every

x

(a,b)

(d)

f(x)<0

for at least one

x

(a,b)