Let a differentiable function have derivative satisfying • for • for At which set of…

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

Let a differentiable function

f

have derivative

f'

satisfying •

f'(x)>0

for

x<-1

and

x>3

•

f'(x)<0

for

-1<x<3

At which set of

x

–values is

f

most likely to attain a local maximum and a local minimum, respectively? (a) local maximum at both

x=-1

and

x=3

(b) local maximum at

x=-1

, local minimum at

x=3

x=3

, local minimum at

x=-1

(d) local minimum at both

x=-1

and

x=3