How to find the minimum of $f(x)=\frac{4x^2}{\sqrt{x^2-16}}$ without using the derivative? 
Find the minimum of function $$f(x)=\frac{4x^2}{\sqrt{x^2-16}}$$ without using the derivative.

In math class we haven't learnt how to solve this kind of problems (optimization) yet. I already know that is solvable using derivatives, but there should be another way. Thanks in advance!

Substitution makes it easier: Write $t=x^2-16$ then using inequality between AG and GM we have $$\frac{4x^2}{\sqrt{x^2-16}}=\frac{4t+64}{\sqrt{t}}\geq {4\sqrt{16t}\over \sqrt{t}}=16$$
and the minimum is achieved at $t=16$ or $x =\pm 4\sqrt{2}$
