For a continuous function

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

Problem

f

, the derivative satisfies

f'(x)>0

for

x<2

f'(2)=0

, and

f'(x)<0

for

x>2

. Which of the following best describes the behavior of

f

x=2

? (a)

f

has a point of inflection at

x=2

because the sign of

f'(x)

changes there. (b)

f

has a local minimum at

x=2

because the sign of

f'(x)

changes from positive to negative. (c)

f

has a local maximum at

x=2

because the sign of

f'(x)

changes from positive to negative. (d) The information is insufficient to determine whether

f

has a local extremum at

x=2