Problem 1311 (difficulty: 4/10)

Let \(\displaystyle f: \R^p \rightarrow\R^q\) be differentiable at the points of the interval \(\displaystyle [a,b]\subset\R^p\). Prove that

\(\displaystyle |f(b)-f(a)| \le |b-a| \cdot \sup_{c\in[a,b]} ||f'(c)||. \)

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