Consider f(x)=x2sin(1/x)f(x) = x^2 \sin(1/x)f(x)=x2sin(1/x) for x≠0x \neq 0x=0 and f(0)=0f(0) = 0f(0)=0. Is fff differentiable at x=0x=0x=0?
Yes, f′(0)=0f'(0) = 0f′(0)=0
No, the derivative doesn't exist
Yes, f′(0)=1f'(0) = 1f′(0)=1
No, fff isn't even continuous at 000