Mean Value Theorem Proof

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Want to use the mean value theorem? Prove it.
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Just in case anyone was confused (as I was) how we know that h(a) and h(b) are equal to zero: At points a and b the curves intersect, meaning f(a) = g(a) and f(b) = g(b). Since h(a) = f(a) - g(a), h(a) = 0 and h(b) = f(b) - g(b), h(b) = 0

kingedwardtherd
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Very interesting how without Rolle's Theorem this would not work!

EpicSelenium
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Super succinct and elegant! Thank you ~

kathymckenzie
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I got lost on why is g'(c) = [g(b)- g(a)]/[b - a]

donlydSkYiSfaLLing
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Very neat, I understood perfectly! Thank you!

bengisukubra