For a continuous function

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

Problem

f

, suppose

f(x)<0

for all

1<x<4

. Define

A(t)=\int_{0}^{t} f(x)\,dx

. Which statement about

A

is true on the interval

1<t<4

? (a)

A

\;is increasing throughout

(1,4)

. (b)

A

\;attains an absolute minimum at

t=4

. (c)

A

\;is decreasing throughout

(1,4)

. (d)

A

\;is decreasing and concave up on

(1,4)