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This question from a previous multivariable calculus exam.I don't know how to start with this question:

Let $f$ be differentiable at every point of line segment joining $x_0$ and $x_0+h$.Show that there is a number $s\in (0,1)$ ,such that

$f(x_0+h)-f(x_0)=f'(x_0+sh).h$

Please help with some hint for how to go for the answer to question...

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    $\begingroup$ Mean value theorem? $\endgroup$ – EricAm Sep 26 '14 at 10:49
  • $\begingroup$ Have a look here $\endgroup$ – Vera Sep 26 '14 at 10:50
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Hint. Use the Mean Value Theorem to the function $$ g(t)=f(x_0+th), \quad t\in [0,1]$. $$ Then $$ f(x_0+h)-f(x_0)=g(1)-g(0)=g'(s), \quad \text{for some}\,\,\,s\in (0,1). $$

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  • $\begingroup$ thanks, after reading comments I still did not know how to apply definition but your answer really helped... $\endgroup$ – spectraa Sep 26 '14 at 10:59

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