Let be a twice-differentiable function such that • for for Define

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let

f

be a twice-differentiable function such that •

f'(x)>0

for

x<-2

•

f'(x)<0

for

-2<x<5

•

f'(x)>0

for

x>5

Define

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

. On which interval is

F

concave down? (a)

(-\infty,-2)\cup(5,\infty)

(b)

(-2,5)

(c)

(-2,\infty)

(d)

(-\infty,5)