Singular points

Stationary points of $f(x)$ occur at values of $x$ in the interior of the domain where the derivative is not defined. To locate singular points, find interior points $x$ where $f'(x)$ is not defined but $f(x)$ is defined

Example
Let $f(x) = 3(x - 1)^{1/3}.$ Then

$f'(x) = (x - 1)^{-2/3} = \dfrac{1}{(x - 1)^{2/3}}.$

$f'(1)$ is not defined, although $f(1)$ is defined. Thus, the (only) singular point occurs at $x = 1.$ The corresponding singular point on the graph is

$(1, f(1)) = (1, 0).$