Real analysis

the Extende Mean Value Theorem(EMVT) states that, if f and g are continous on [a,b] and differentiable on (a,b), then there exists a point c in (a,b)such that g'(c)(f(b)-f(a))=f'(c)(g(b)-g(a)). Prove this Theorem. (Hint: Use the function h(x)=f(x)(g(b)-g(a))-g(x)(f(b)-f(a)).

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