Suppose a twice–differentiable curve has the following qualitative features: •…

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

Problem

Suppose a twice–differentiable curve

C

has the following qualitative features: •

C

decreases for

x<0

, has a horizontal tangent at

x=0

, and increases for

x>0

. •

C

is concave down on

(-\infty,0)

and concave up on

(0,\infty)

. Curve

D

is negative on

(-\infty,0)

, zero at

x=0

, positive on

(0,\infty)

, and changes from decreasing to increasing at

x=0

. Curve

E

is negative on

(-\infty,0)

, zero at

x=0

, positive on

(0,\infty)

, and is increasing everywhere. Identify which curve represents

f

, which represents

f'

, and which represents

f''

. Give your answer in the form

f=\_,\;f'=\_,\;f''=\_

(use

C

D

, or

E