Mathematics

Problem

A continuous function

g

satisfies:

g'(x)<0

for

x<1

g'(1)=0

g'(x)>0

for

1<x<4

g'(4)=0

, and

g'(x)<0

for

x>4

. Classify the points

x=1

and

x=4

as local maxima, local minima, or neither for

g