Solution
= Solution
The <derivative> is
$$
f'(x)=\frac{2x}{a^2}-\frac{2a^2}{x^3}.
$$
A <stationary point> at $x=1$ requires $2/a^2-2a^2=0$, or $a^4=1$. Since $a>0$, $\boxed{a=1}$.
= Solution
The <derivative> is
$$
f'(x)=\frac{2x}{a^2}-\frac{2a^2}{x^3}.
$$
A <stationary point> at $x=1$ requires $2/a^2-2a^2=0$, or $a^4=1$. Since $a>0$, $\boxed{a=1}$.