# Suppose a multivariable function f:R^n->R is concave and sufficiently smooth. We have: ∥f(x)−f(x0)∥<=M∥x−x0∥ for some positive constant M.

Suppose a multivariable function $f:{\mathbb{R}}^{n}\to \mathbb{R}$ is concave and sufficiently smooth. We have:
$‖f\left(\mathbf{x}\right)-f\left({\mathbf{x}}_{0}\right)‖\le M‖\mathbf{x}-{\mathbf{x}}_{0}‖$ 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?
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zupa1z
This is the definition of Lipschitz continuity. $M$ is called the Lipschitz constant of $f$.
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