Let \( f \) be continuous on \( [a, b], a0 \), and differentiable on \( (a, b) \). Prove that th...

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Let \( f \) be continuous on \( [a, b], a0 \), and differentiable on \( (a, b) \). Prove that there exists \( c \in(a, b) \) such that \( \frac{b f(a)-a f(b)}{b-a}=f(c)-c f^{\prime}(c) \)
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