Question: Show that if f(x) > 0 on (a, b) (that is, if f is convex on [a, b]), then for any natural numbers m, n

Show that if fʹʹ(x) > 0 on (a, b) (that is, if f is convex on [a, b]), then for any natural numbers m, n we have Mn(f) < ∫ba f(x)dx < Tm(f): If fʹʹ(x) < 0 on [a, b], this inequality is reversed.

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