Question

Graph: f(x)=-x^3+6x^2-9x-4
-find the intervals on which the function is increasing and decreasing.
-find all maximum and minimum values.

Answer 1

Okay, first take the first derivative.

Answer 2

Cubic equation. Should have three f(x) = 0 solutions.
Get max, min from df/dx = 0 solutions.
Check using second derivatives. (>0 means at a min, < 0 means at a max.).

d(x^n)/dx = n x^(n-1)

Home free...almost.