Question Number 94125 by i jagooll last updated on 17/May/20
![Given a function H(x) = ∣sin x+cos x∣ + (√2) cos x with x ∈ [ 0, 2π ] find H(x)_(max) and H(x)_(min)](https://www.tinkutara.com/question/Q94125.png)
$$\mathrm{Given}\:\mathrm{a}\:\mathrm{function}\: \\ $$$$\mathrm{H}\left(\mathrm{x}\right)\:=\:\mid\mathrm{sin}\:\mathrm{x}+\mathrm{cos}\:\mathrm{x}\mid\:+\:\sqrt{\mathrm{2}}\:\mathrm{cos}\:\mathrm{x} \\ $$$$\mathrm{with}\:\mathrm{x}\:\in\:\left[\:\mathrm{0},\:\mathrm{2}\pi\:\right]\: \\ $$$$\mathrm{find}\:\mathrm{H}\left(\mathrm{x}\right)_{\mathrm{max}} \:\mathrm{and}\:\mathrm{H}\left(\mathrm{x}\right)_{\mathrm{min}} \\ $$
Answered by john santu last updated on 17/May/20
$$\mathrm{H}\left(\mathrm{x}\right)_{\mathrm{max}} \:=\:\sqrt{\mathrm{4}+\mathrm{2}\sqrt{\mathrm{2}}}\:,\mathrm{when}\:\mathrm{x}\:=\:\frac{\mathrm{3}\pi}{\mathrm{8}} \\ $$$$\mathrm{H}\left(\mathrm{x}\right)_{\mathrm{min}} \:=\:\mathrm{1}−\sqrt{\mathrm{2}}\:,\:\mathrm{when}\:\mathrm{x}\:=\:\pi \\ $$