QQ on Max/Min (1 Viewer)

[Paradoxica]

If a part of a question says something like "find the maximum/minimum of R(x)" where R(x) = O(x) + P(x)/Q(x) (a.k.a. some rational function), is it acceptable to quickly prove AM-GM, and then proceed to use AM-GM to find the minimum/maximum value of the function? Of course, I am assuming there is no hence, or if there is, it is hence or otherwise.

 

[Paradoxica]

e.g. find the local maximum and minimum values of (in this case, weight the 1/x term and use am-gm for n=4) or only find the local minimum and then make an argument from symmetry.