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http://en.wikipedia.org/wiki/Darboux%27s_theorem_%28analysis%29

I'm having a bit of trouble understanding the proof of Darboux's Theorem on the IVP of derivatives.

Why should there be an extremum such that $g'(x) = 0$ from the fact that $g'(a)>0$ and $g'(b)<0$ ?

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    What is $g$? The wikipedia page uses $f$ and $\phi$...2012-09-07
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    I can't understand what you mean by "...only a maximum".2012-09-07

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