When deriving you have to keep in mind that the derivative of (1-x)^2 is -2(1-x) which is negative and instead of

you should get this:

Also, you are correct that -1 and 1 are both zeros but you can't just assume those are the only ones.

which simplifies to:

and eventually simplifies to reveal a third zero of x = .

You should find that the function is increasing from x = {-infinity,1/5},{1,infinity} and decreasing from x = {1/5,1} As shown in the graph of f.