The second derivative of a differentiable function satisfies for

MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

The second derivative of a differentiable function

f

satisfies

f''(x)>0

for

-3<x<1

and for

x>5

, while

f''(x)<0

for

1<x<5

. In addition,

f''(x)=0

x=-3,1,5

and

f''

changes sign at each of those

x

-values. State the open intervals on which the graph of

f

is concave up, and list the

x

-values at which

f

has points of inflection.