critical point

A point in a function's domain where its derivative is zero or undefined — the only places extrema can occur.

A critical point of $f$ is a value $c$ in the domain of $f$ where $f'(c)=0$ or $f'(c)$ does not exist. By Fermat's theorem, every local extremum occurs at a critical point, though not every critical point is an extremum.

Examples

For $f(x)=x^3-3x$ : $f''(x)=3x^2-3=0$ at $x=\pm1$ , so $x=\pm1$ are critical points.