Let . Which statement about the critical points of is…

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

Problem

Let

f(x) = x^{4} - 4x^{3}

. Which statement about the critical points of

f

is correct? (a)

x=0

is a local maximum, and

x=3

is a local minimum (b)

x=0

is a critical point that is not a local extremum, whereas

x=3

is a local minimum (c)

x=0

is not a critical point, while

x=3

is a local minimum (d) Neither

x=0

nor

x=3

is a critical point because

f''(x)

exists at both points