question archive Let f: R - R be convex (and hence continuous)
Let f: R - R be convex (and hence continuous)
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Let f: R - R be convex (and hence continuous). Then ( Va <b) f(x) d. < f(a) + f(b) * ) b - a Ja 2 (i) (MATH 563 only) Prove the Hermite-Hadamard inequalities. Hint: If r E [a, b], then write r = : a+ ab. Now use Jensen's inequality and integrate. (ii) (MATH 461 only) Apply (*) to f(x) = exp(x) and simplify the resulting inequality. What do we get if we further set u := exp(a) and v := exp(b)?
