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Let $f:[a,b] \to \mathbb{R}^n$ be a smooth curve such that the estimate $\|f'(t)\| \leq f'(t)$ holds. Show that the estimate $\|f(b) - f(a)\| \leq f(b) - f(a)$ also holds.

I was started to use the mean value theorem because this appears to prove this straight away but then I remembered that we only defined the mean value theorem for a function $f:D \to \mathbb{R}$ where $D \subset \mathbb{R}^n$, is there another way of doing this?

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    I think you need to answer @PeteL.Clark's question first.2012-05-19

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