Question Number 81763 by Khyati last updated on 15/Feb/20
$${Q}.\:{Find}\:{the}\:{minimum}\:{value}\:{of}\: \\ $$$$\mathrm{3}{cosx}\:+\:\mathrm{4}{sinx}\:+\:\mathrm{8}. \\ $$
Commented by john santu last updated on 15/Feb/20
$${f}\left({x}\right)=\:\mathrm{3cos}\:{x}+\mathrm{4sin}\:{x}+\mathrm{8} \\ $$$${f}\left({x}\right)\:=\:\sqrt{\mathrm{9}+\mathrm{16}}\:\mathrm{cos}\:\left({x}−\theta\right)+\mathrm{8}\:,\:{where}\:\theta=\mathrm{tan}^{−\mathrm{1}} \left(\frac{\mathrm{4}}{\mathrm{3}}\right) \\ $$$${f}\left({x}\right)=\:\mathrm{5cos}\:\left({x}−\theta\right)+\mathrm{8} \\ $$$${minimum}\:{value}\:{is}\:−\mathrm{5}+\mathrm{8}\:=\:\mathrm{3} \\ $$
Commented by Khyati last updated on 16/Feb/20
$${Do}\:{you}\:{have}\:{any}\:{other}\:{method}\:{except} \\ $$$${differentiation}\:?? \\ $$