Mathematics

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.