Let . Which of the following best describes the nature of its critical…

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

Problem

Let

f(x)=x^{4}-8x^{3}+18x^{2}

. Which of the following best describes the nature of its critical points? (a)

x=0

is a local maximum, and

x=3

is a local minimum. (b)

x=0

is a local minimum, and

x=3

is not a local extremum. (c)

x=0

is a local minimum, and

x=3

is a local maximum. (d) Neither

x=0

nor

x=3

is a local extremum, because

f'(x)

does not change sign at either point.