1) Find the critical number for

I must be doing something wrong with finding the derivative of that function because I end up with

, so my critical numbers were 0, -1 and 1. But the given answer was 1 and -1. Why was the zero neglected? It made the derivative equal to zero, which should've made it a critical number.

the function is undefined at x = 0
2)

The given answer says that there are no critical numbers and the function is increasing. I don't understand why. The derivative gave me 1 / (3(x-1)^(2/3) so shouldn't 0 be a critical number because it made the function undefined?

the derivative is undefined at x = 1 , not 0