<s>[INST] How to find the maximum value of $3^x + 5^x - 9^x + 15^x - 25^x$ as $x$ varies over the reals? 
How to find the maximum value of  $3^x + 5^x - 9^x + 15^x - 25^x$ as x
  varies over the reals ?

Suggestions please!
 [/INST] $$f(x)-1=3^x + 5^x - 9^x + 15^x - 25^x-1=-\frac{1}{2}\left( (3^x-1)^2+(5^x-3^x)^2+(1-5^x)^2\right) \leq 0$$
Second solution By C-S inequality
$$(3^x+5^x+15^x)^2 \leq (1 +5^x+3^x)( 3^x+1+5^x) $$
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