Let be differentiable on an interval

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

Problem

Let

f

be differentiable on an interval

I

, and define the accumulation function

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

. Which of the following statements correctly describes where

F

is concave up? (a)

F

is concave up where

f''(x)>0

. (b)

F

is concave up where

f'(x)>0

. (c)

F

is concave up where

f(x)>0

. (d)

F

is concave up where

f'(x)<0