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Question Number 31712 by gunawan last updated on 13/Mar/18
![let f convex function on [0, 2π] with f ′′(x) ≤ M . find values a and b so a≤∫_0 ^(2π) f(x)cos x dx ≤bM](Q31712.png)
$$\mathrm{let}\:{f}\:\mathrm{convex}\:\mathrm{function}\:\mathrm{on}\:\left[\mathrm{0},\:\mathrm{2}\pi\right] \\ $$$$\mathrm{with}\:{f}\:''\left({x}\right)\:\leqslant\:{M}\:. \\ $$$$\mathrm{find}\:\mathrm{values}\:{a}\:\mathrm{and}\:{b}\:\:\mathrm{so} \\ $$$${a}\leqslant\int_{\mathrm{0}} ^{\mathrm{2}\pi} {f}\left({x}\right)\mathrm{cos}\:{x}\:{dx}\:\leqslant{bM} \\ $$