nobody wanna help me? all i know that if a function is differentiable at point a then the limit lim(h->0) (f(a+h)-f(a))/h exists but i tried doing this with some random function that is obviously not differentiable at some point and yet i managed to prove that it is differentiable which obviously means that i have done something wrong. so can somebody please give me a hand showing f(x) from the previous post (piecewise function btw) is diff or not diff at x=0. any help is appreciated.