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Question Number 94125 by i jagooll last updated on 17/May/20

$$\mathrm{Given}\mathrm{a}\mathrm{function}$$$$\mathrm{H}\left(\mathrm{x}\right)=\mid \sin \mathrm{x}+\cos \mathrm{x}\mid +\sqrt{2}\cos \mathrm{x}$$$$\mathrm{with}\mathrm{x}\in [0,2\pi ]$$$$\mathrm{find}\mathrm{H}{\left(\mathrm{x}\right)}_{\max }\mathrm{and}\mathrm{H}{\left(\mathrm{x}\right)}_{\min }$$

Answered by john santu last updated on 17/May/20

$$\mathrm{H}{\left(\mathrm{x}\right)}_{\max }=\sqrt{4+2\sqrt{2}},\mathrm{when}\mathrm{x}=\frac{3\pi }{8}$$$$\mathrm{H}{\left(\mathrm{x}\right)}_{\min }=1-\sqrt{2},\mathrm{when}\mathrm{x}=\pi$$

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