Level Set

Definition

Consider a function $f:{\mathbb{R}}^n\to \mathbb{R}$, then the level set of $f$ is defined as $L_c(f)=\{(x_1,x_2,\dots ,x_n)|f(x_1,x_2,\dots ,x_n)=c\}$

Facts

When $n=2$, the tangential line to a level curve at the point $(x_0,y_0)$ is defined as $f_x(x_0,y_0)(x-x_0)+f_y(x_0,y_0)(y-y_0)=0$