$\Vert f(\mathbf{x})-f({\mathbf{x}}_{0})\Vert \le M\Vert \mathbf{x}-{\mathbf{x}}_{0}\Vert $ for some positive constant $M$.

If the $f$ is univariate, we know that $M$ is the absolute value of the slope of the tangent line at ${\mathbf{x}}_{0}$. But what is it for multivariable case, is there a special name in math given to it?