I am reading the proof for the M.V.T, mostly understanding it all, except for this one step. Here is the link to it: http://tutorial.math.lamar.edu/Classes/CalcI/DerivativeAppsProofs.aspx#Extras_DerAppPf_MVT(adsbygoogle = window.adsbygoogle || []).push({});

It's near the bottom of the page.

What I don't precisely is why they create a new function, g(x), which is defined as f(x) subtracted by the equation for the secant line. A few steps after this they are able to redefine the interval (a, b) for this new function g(x), where the endpoints are equal to equal to each other, but I just don't understand the motive for this. What does it accomplish in proving this theorem?

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# Mean Value Theorem Proof

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