Question Number 11050 by lepan last updated on 09/Mar/17
$${The}\:{function}\:{f}\left({x}\right)={acosx}+{b}\:{where} \\ $$$${a}<\mathrm{0}\:{has}\:{a}\:{maximum}\:{value}\:{of}\:\mathrm{8}\:{and} \\ $$$${a}\:{minimum}\:{value}\:{of}\:−\mathrm{2}.\boldsymbol{{F}}{ind}\:{a}+{b}. \\ $$$$ \\ $$$$ \\ $$$$ \\ $$
Answered by Mahmoud A.R last updated on 09/Mar/17
$$−\mathrm{1}\:\leqslant\:\mathrm{cos}{x}\:\leqslant\:\mathrm{1}\: \\ $$$$−\:{a}\:\geqslant\:{a}\mathrm{cos}{x}\:\geqslant\:{a} \\ $$$${b}\:−{a}\:\geqslant\:{a}\mathrm{cos}{x}\:+\:{b}\:\geqslant\:{a}\:\:+\:{b} \\ $$$${minimum}\:{of}\:{f}\left({x}\right)\:=\:{a}\:+\:{b}\:=\:−\mathrm{2} \\ $$