# Definitions > [!NOTE] Definition (Critical Point of a Surface in $\mathbb{R}^{3}$) > Let $f:U\subset \mathbb{R}^{2}\to \mathbb{R}$ be [[Real-Valued Function on Real n-Space (Multivariable Function)|multivariable function]]. Let $(a,b)\in \mathbb{R}^{2}.$ Then $(a,b)$ is a **critical point** of $f$ iff the [[Fréchet Differentiation|gradient]] of $f$ at $(a,b)$ is $(0,0).$ > # Properties **Classification**: .... # Applications In real-world applications, the local extrema of a multivariable function are not usually obtained by differentiation or the second derivative test, because the form of the function $f(x, y)$ may not be known explicitly. Instead, a numerical method called [[Method of Steepest Descent|steepest ascent/descent]] is employed.