How do you find decreasing intervals of

Question

6x^3-63x^2-144x-2?

I found my increasing intervals from placing the derivatives i just can't seem to solve for the decrease

Answer 1

f decreasing means f' < 0

f' = 18x^2 - 126x - 144
= 18(x^2-7x-8)
= 18(x+1)(x-8)
Since that is a parabola which open upward, f' is negative between the roots.

f(x) is decreasing on the interval (-1,8)

This can be verified by looking at the graph:

http://www.wolframalpha.com/input/?i=6x^3-63x^2-144x-2