Give a proof of the Cauchy's Mean Value Theorem by considering the function F(æ) = [f(b) – f(a)]g(x) – [g(b) – g(a)]f(x). (Remember to check all the conditions whenever applying any Mean Value...

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Extracted text: Give a proof of the Cauchy's Mean Value Theorem by considering the function F(æ) = [f(b) – f(a)]g(x) – [g(b) – g(a)]f(x). (Remember to check all the conditions whenever applying any Mean Value Theorem.)