The second derivative of a twice-differentiable function satisfies for for

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

Problem

The second derivative of a twice-differentiable function

g

satisfies

g''(x)>0

for

x<-1

g''(-1)=0

g''(x)<0

for

-1<x<3

g''(3)=0

, and

g''(x)>0

for

x>3

. On which interval is the graph of

g

concave down? (a)

[-1,3]

(b)

(-\infty,-1)\cup(3,\infty)

(c)

(-1,3)

(d)

(-1,\infty)