1. Let f(x)= {x^2 sin (1/x) when x≠0 and 0 when x=0
[b]2. Find f'(x). Does it exist for every x? (Hint: the case when x=0 needs special attention)
[b]3. What I did is, I found the derivative of x^2 sin (1/x). That is, 2xsin(1/x)-cos(1/x). Then I figured the derivative of 0 is just 0...