Find the maximum of $f(x) = \dfrac{x^4-x^2}{x^6+2x^3-1}$ where $x>1$.
In my previous post(optimization-contest-problem), I showed you the way of approaching this particular problem with the most comfortable and familiar method (calculus method) that it would spring first to students' mind, a method that students' from all four corners of the world are inclined to use.