Find the relative extrema of [tex] f(x)=|3x-x^2|[/tex]. Normally you solve f'(x)=0 to find the critical points, in that case we have 3-2x=0 => x=3/2. However there are two other relative extrema that I cannot find by calculus as the absolute nature of f(x) has confused me. Indeed doing a sign analysis on the points x=0 and 3; shows that these points are not extrema points! I am studing on my own, Please help, Thanks.