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Let $U$ be a convex open set in $\mathbb{R}^n$ and $f:U\longrightarrow \mathbb{R}$ such that $ \left| \large \frac{\partial f}{\partial x_i}(x)\right| \le M (\text{constant}) \; ,\forall x\in U$ and $\forall i=1\,,\cdots ,n.$ Prove that $|f(x)-f(y)|\le M||x-y||_1$ (1-norm) $\forall x,y \in U$

$\large{\frac{\partial f}{\partial x_i}}:$ Partial derivatives

$f:$ not necessarily differentiable

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