Menu Close

The-function-f-x-acosx-b-where-a-lt-0-has-a-maximum-value-of-8-and-a-minimum-value-of-2-Find-a-b-




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

Leave a Reply

Your email address will not be published. Required fields are marked *