1. The problem statement, all variables and given/known data 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) = (1-x)2 (1+x)3 2. Relevant equations Now when get to have the first derivative by multiplication rule f'(x) = g(x)*h'(x)+h(x)*g'(x): f'(x) = ((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?