$ Let f(z) = (Re(z))^3 + (Im(z))^3$
(a) At which points (if any) is f differentiable? Find the expression of f' at those points.
(b) Draw a picture of the subset of C consisting of those points at which f is differentiable. Hence decide at which points (if any) f is analytic.
$ f(z) = x^3 + y^3 $
(a) Using Cauchy Riemann equations I found that f is only differentiable at (0,0). And f' is 0 at that point.
(b) f is nowhere analytic as it is not differentiable in an $\epsilon$ neighbourhood of z.
Is that correct?