Mathematics

Mathematics

Problem

A differentiable function

g

satisfies

g'(x)<0

for

x<3

and

g'(x)>0

for

x>3

. Which of the following is CORRECT? a)

g

is increasing on

(-\infty,3)

and decreasing on

(3,\infty)

;

x=3

is a point of local maximum. b)

g

is decreasing on

(-\infty,3)

and increasing on

(3,\infty)

;

x=3

is a point of local minimum. c)

g

is decreasing on

(-\infty,3)

and increasing on

(3,\infty)

;

x=3

is an inflection point. d)

g

is decreasing on

(-\infty,3)

and increasing on

(3,\infty)

;

x=3

is a point of local maximum.

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