Question: 4. Let f,g : [a,b] R be continuous and differentiable on (a,b). Prove that there exists c R s.t. f'(c)(g(b) g(a)) = g'(c)(f(b) f(a)). Hint:

4. Let f,g : [a,b] R be continuous and differentiable on (a,b). Prove that there exists c R s.t. f'(c)(g(b) g(a)) = g'(c)(f(b) f(a)). Hint: We could rewrite this as F6) - fl@) _ g(b) g(a) g'(c) provided there is no division by zero. Therefore this is called the Generalized Mean Value Theorem. To prove it, study the function f(z)(g(b) g(a)) g(z)(f(b) f(a))

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