1. $E_N = -Ar^{-1} + Br^{-n}$
$\dfrac{dE_N}{dr} = Ar^{-2} - n \cdot Br^{-(n+1)} = \dfrac{A}{r^2} - \dfrac{n \cdot B}{r^{n+1}}$
$\dfrac{dE_N}{dr} = 0 \implies \dfrac{A}{r^2} = \dfrac{n \cdot B}{r^{n+1}}$
2. since $r > 0$ ...
$A = \dfrac{n \cdot B}{r^{n-1}} \implies r^{n-1} = \dfrac{n \cdot B}{A}$
$r_0 = \left(\dfrac{n \cdot B}{A}\right)^{\frac{1}{n-1}}$
I'll let you complete part 3 on your own ...