Suppose is differentiable on and satisfies for

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

Problem

Suppose

s

is differentiable on

\mathbb R

and satisfies

s'(x)>0

for

x<3

and

s'(x)<0

for

x>3

. Identify (i) the open interval(s) on which

s

is increasing and (ii) the critical number where the change in monotonicity occurs.