A differentiable function satisfies the following: • is decreasing on

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

Problem

A differentiable function

f

satisfies the following: •

f

is decreasing on

(-\infty,-3)

, increasing on

(-3,1)

, and decreasing on

(1,\infty)

. •

f

is concave up on

(-\infty,0)

and concave down on

(0,\infty)

. Identify all

x

-values where

f'(x)=0

, and state whether

f'(x)

is positive or negative on each of the open intervals determined by these zeros.