Consider the Function

Question

Consider the function f(x)=x³-9x².

a. Find a formula for f'(x).

b. Use your answer to part (a) to find any critical points of f.

c. Use either the first or second derivative test to classify any critical points from part (bO as either a local min or a local max. explain your reasoning so that the use of the first or second derivative is clear.

Answer 1

f'(x)=3x²-18x

and f"(x)=6x-18

The possible critical points are x=0 and x=6

You answer part c! And if you are unsure, graph the original equation.