Mean value inequality
= Mean value inequality
If the line segment from $x$ to $y$ lies in the domain of a differentiable map and $\lVert Df_z\rVert\leq M$ along it, then
$$
\lVert f(y)-f(x)\rVert\leq M\lVert y-x\rVert.
$$
= Mean value inequality
If the line segment from $x$ to $y$ lies in the domain of a differentiable map and $\lVert Df_z\rVert\leq M$ along it, then
$$
\lVert f(y)-f(x)\rVert\leq M\lVert y-x\rVert.
$$