\begin{align*} M''(0) & = -\frac{{\left(r - 2\right)} r {\left(-2 \cdot 0 + 1\right)}^{\frac{1}{2} r - 2}}{{\left(-2 \cdot 0 + 1\right)}^{r}} + \frac{2 r^{2} {\left(-2 \cdot 0 + 1\right)}^{r - 2}}{{\left(-2 \cdot 0 + 1\right)}^{\frac{3}{2} r}} \\ & = -\frac{{\left(r - 2\right)} r }{1} + \frac{2 r^{2} }{1}= 2r + r^2 = \sigma^2 + \mu^2 \end{align*}