The problem goes something like this:
$$ f(x) = 4^x+8^x+9^x-2^x-6^x-12^x$$Find the maximum value of f(x).
This question appeared on a test in which calculators were not allowed, so please refrain from using any graphing calculators or similar instruments.
I tried substituting $2^x=\alpha$ and $3^x=\beta$ to see if I could then observe something. It was of no help to me.
Any ideas or solutions would be appreciated.