Mathematics

Problem

Curves M, N, and P are defined on

(-\infty,\infty)

with the following properties: • Curve M has

x

-intercepts at

x=-2

and

x=2

and a local maximum at

x=0

. • Curve N crosses the

x

-axis at

x=-2

0

, and

x=2

; it is positive on

(-2,0)

and negative on

(0,2)

. • Curve P is negative on

(-2,2)

and positive elsewhere. Assuming the three curves are

f

f'

, and

f''

for the same twice-differentiable function

f

, identify each curve.