Question: Let f be a real valued function on R. Suppose that f has a finite derivative for every x [a, b], and that f '

Let f be a real valued function on R. Suppose that f has a finite derivative for every x [a, b], and that f ' is integrable over [a, b]. Prove that x f ( x ) f (a ) f ' for all x [a, b]. a Note that the integration and differentiation done is Lebesgue integration and measure theory Real Analysis , Royden \f\f

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