A function is defined by

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

Problem

A function

g

is defined by

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

, where

f

is continuous. At

x=5

, one has

f(5)=0

, with

f(t)<0

for

t<5

sufficiently close to

5

and

f(t)>0

for

t>5

sufficiently close to

5

. Which statement best describes the behavior of

g

x=5

? (a)

g

has a local maximum at

x=5

. (b)

g

has a point of inflection at

x=5

. (c)

g

has a local minimum at

x=5

. (d)

g

is neither increasing nor decreasing near

x=5