Suppose is differentiable for all real numbers and satisfies and

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

Problem

Suppose

f

is differentiable for all real numbers and satisfies

f'(2)=0

and

f''(2)=0

. A sign chart for

f'

shows

f'(x)<0

when

x<2

and

f'(x)>0

when

x>2

. Which of the following best describes the point

x=2

? (a)

x=2

is a point of inflection of

f

. (b)

x=2

is a local maximum of

f

. (c)

x=2

is a local minimum of

f

. (d) No conclusion about extrema can be drawn from the given information.