f(x) = x sin(1/x) for every x not equal to 0
0 for x = 0
How do i show whether this function is differentiable or not at x=0. First of all i know that if a function is differentiable at a then lim(h->0) (f(a+h)-f(a))/h has to exist or rather lim(x->a) (f(x)-f(a))/(x-a). I was pretty sure that the function was not differentiable at x=0 until i plugged it into my graphics calc to have a look at the graph, need an explanation for this please.