Consider the function f(x) = -2 x^3 + 24 x^2 - 72 x + 1.?

Question

For this function there are three important intervals (-infinity, A], [A,B], and [B,infinity) where A and B are the critical numbers.

Find A and B

Also, find where f(x) is increasing and where its decreasing (intervals)

Answer 1

A = 2, B = 6

dec from -00 to 2, inc from 2 to 6 , dec from 2 to 00

Answer 2

Hint:
A function y=f(x) has critical points at all points x(0) where f'(x(0))=0 or f(x) is not differentiable.
-