A twice-differentiable function has the following qualitative behavior: • is…

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

Problem

A twice-differentiable function

f

has the following qualitative behavior: •

f

is decreasing and concave down on

(-\tfrac{\pi}{2},-3)

; •

f

is decreasing and concave up on

(-3,0)

; •

f

is increasing and concave up on

(0,2)

; •

f

is increasing and concave down on

(2,\tfrac{\pi}{2})

. List the sign of

f'(x)

and of

f''(x)

on each interval determined by

x=-3

x=0

, and

x=2

, and state the

x

-values where

f'(x)

attains a local maximum or minimum.