$f \prime \prime(x)=\left(x^2+1\right)^{-\frac{3}{2}}+(x+1)\left(-\frac{3}{2}\right)\left(x^2+1\right)^{-\frac{5}{2}} \cdot 2 x$
$f \prime \prime(x)=\left(x^2+1\right)^{-\frac{3}{2}}-3 x(x+1)\left(x^2+1\right)^{-\frac{5}{2}}$
$f \prime \prime(x)=\frac{1}{\sqrt{\left(x^2+1\right)^3}}-\frac{3 x(x+1)}{\sqrt{\left(x^2+1\right)^5}}$
$f \prime \prime(x)=\frac{x^2+1-3 x^2-3 x}{\sqrt{\left(x^2+1\right)^5}}$
$f \prime \prime(x)=\frac{-2 x^2-3 x+1}{\sqrt{\left(x^2+1\right)^5}}$
$f \prime \prime(x) \geq 0 \rightarrow 2 x^2+3 x-1 \leq 0$
$f \prime(x) \geq 0 \rightarrow x \geq \frac{-3-\sqrt{17}}{4} \wedge x \leq \frac{-3+\sqrt{17}}{4}$
e otteniamo due flessi:
$x_{F 1}=\frac{-3-\sqrt{17}}{4}$
$x_{F 2}=\frac{-3+\sqrt{17}}{4}$
