Is zero a critical point for x^3/5?

Dear Student

A critical point is a point at which the derivative of a continuous function is zero or undefined. The given function is continuous and differentiable as well.
Now derivative of given function:
             $\frac{d\left(x^{3/5}\right) }{dx} = \frac{3}{5 x^{2/5}}$  because $\frac{d\left(x^n\right) }{dx} = n{x}^{n-1}$
Now upon filling x as 0 the derivative of function becomes infinite or undefined. Therefore yes zero a critical point for x<sup>3/5.

​​​</sup>Regards