I have to get the following:

- relative extrema of f

- values of f at which the relative extrema occurs

- intervals on which f is increasing

- intervals on which f is decreasing

when f(x) = $\displaystyle (1-x)^2 (1+x)^3$

Now when get to have the first derivative by multiplication rule f'(x) = g(x)*h'(x)+h(x)*g'(x):

f'(x) = $\displaystyle ((1-x)^2)(3(1+x)^2)+((1+x)^3)(2(1-x))$

is it correct to say that f'(x)=0 when x=1 or x=-1?

and if it is, by substituting 1 and -1 to f(x), i'll arrive on ordered pairs' (1,0),(-1,0) which are on a vertical line. when i checked if the interval -1 < x < 1 is increasing or decreasing, i arrived at an answer that it is increasing which is not possible considering the locations of the two critical points.

Where did I go wrong?