INcreasing/Decreasing function

Question

Im having trouble finding the incr/decr values of the function f(x)=x^2(x-1)(x-2) and my first guess was there wasn't an increase decrease change but I searched for help and it did change so im lost on how to solve it

Answer 1

This is a quartic polynomial...graph it!

It has zeros at 0 (double zero) and 1 and 2

It has a maximum at about .x = .61 and a minimum about x = 1.64

The graph will tell you where it is increasing and decreasing.

There are also 2 points of inflection which you can find from the 2nd derivative.