A differentiable function satisfies for

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

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.