A function is differentiable on but not at

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A function

g

is differentiable on

(-\infty,2)\cup(2,\infty)

but not at

x=2

. Suppose

g'(x)<0

for every

x<2

and

g'(x)>0

for every

x>2

. Which of the following must be true? (a)

g

increases on

(-\infty,2)

and decreases on

(2,\infty)

. (b)

g

decreases on the entire real line. (c)

g

decreases on

(-\infty,2)

and increases on

(2,\infty)

. (d)

g

increases on

(-\infty,2)

and also increases on

(2,\infty)