A function is continuous on and differentiable everywhere except at

MATHEMATICS · Subjective · A Level · Mathematics · Differentiation · Differentiation

Problem

A function

g

is continuous on

\mathbb{R}

and differentiable everywhere except at

x=4

. Its derivative satisfies: •

g'(x)<0

for

x<0

, •

g'(0)=0

, •

0<g'(x)\le 5

for

0<x<4

, •

g'(4)

does not exist, •

g'(x)<0

for

x>4

. a) State the open interval(s) on which

g

is strictly increasing. b) State the open interval(s) on which

g

is strictly decreasing. c) Classify

x=0

and

x=4

as points of local maximum, local minimum, or neither, giving one reason for each.