A twice–differentiable function satisfies the following conditions about the sign of…

MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A twice–differentiable function

p

satisfies the following conditions about the sign of its first derivative: •

p'(x)<0

for

x<-2

•

p'(x)>0

for

-2<x<1

•

p'(x)<0

for

1<x<4

•

p'(x)>0

for

x>4

(a) Using only the information provided above, identify the

x

–values at which

p

attains a relative maximum, the

x

–values at which

p

attains a relative minimum, and any relevant values at which

p

attains neither. Provide a written justification that references the behavior of

p'

. (b) Sketch a possible graph of

p

that is consistent with the given information. Clearly label all points corresponding to the relative extrema identified in part (a).