$A = 15-(16x^2+\dfrac{1}{x^2})$
Ta có $16x^2+\dfrac{1}{x^2} \geq 2\sqrt[]{16x^2.\dfrac{1}{x^2}} = 8$
$\Rightarrow A \leq 15-8 = 7$
$\Rightarrow maxA = 7 \Leftrightarrow 16x^2=\dfrac{1}{x^2}$
$\Leftrightarrow x^4=\dfrac{1}{16}$
$x > 0 \Rightarrow x=\dfrac{1}{2}$