1. The problem statement, all variables and given/known data f(x)= xsin(1/x) if x!=0 = 0 if x=0 does the derivative exist at x=0? Can somebody please provide a visual backup of the result? Is this supposed to be a cusp that's why there is no derivative on a continuous function? 2. Relevant equations 3. The attempt at a solution Using the squeeze theorem we see that the function is continuous at 0, but when we compute the derivative limit, we are left with limit[h->0]sin(1/h) which doesn't exist.