Consider f(x)=xsin(1/x)f(x) = x \sin(1/x)f(x)=xsin(1/x) for x≠0x \neq 0x=0 and f(0)=0f(0)=0f(0)=0. Which is true about fff at x=0x=0x=0?
Discontinuous.
Continuous but not differentiable.
Not defined.
Differentiable.