R
\renewcommand*{\implies}{\,\Rightarrow\,}
\begin{align*}
R_i(x) &= A_i\,x + B_i - \frac{1}{x}
\\
R'_i(x) &= A_i + \frac{1}{x^2} = 0
\implies
x_\text{max} = \frac{1}{\sqrt{-A_i}}
\\
R_i(x_\text{max}) &= A_i\,\frac{1}{\sqrt{-A_i}} + B_i - \sqrt{-A_i}
= \varepsilon
\refstepcounter{equation}
\tag{\theequation}\label{eq:sympy}
\end {align*}

