what is the critical point for f(x)=x^(1/3)?
A critical point occurs where the first derivative is either zero or does not exist.
First, find the first derivative: f'(x) = (1/3)·x-2/3
The first derivative will be undefined when x = 0.
f(x) = x^(1/3)
f'(x) = (1/3)x^(-2/3) this derivative is undefined when x = 0......so this is a critical point
See the graph here :
As the graph shows......we have vertical tangent at x = 0