Let $\mathrm{f}\left(\mathrm{x}\right)=3^{{\left({\mathrm{x}}^2-2\right)}^3+4},\mathrm{x}\in \mathrm{R}$. Then which of the following statements are true?
P : x = 0 is a point of local minima of $f$

 $\mathrm{Q}:\mathrm{x}=\sqrt{2}$ is a point of inflection of $f$

R :$f\text{'}$ is increasing for $\mathrm{x}>\sqrt{2}$

$\mathrm{f}\left(\mathrm{x}\right)=3^{{\left({\mathrm{x}}^2-2\right)}^3+4}=81\cdot 3^{{\left({\mathrm{x}}^2-2\right)}^3}$
$\begin{array}{l}{\mathrm{f}}^{\mathrm{\prime }}\left(\mathrm{x}\right)=81\cdot 3^{{\left({\mathrm{x}}^2-2\right)}^3}\cdot \log 3\cdot 3{\left({\mathrm{x}}^2-2\right)}^2\cdot 2\mathrm{x}\\ =486\cdot 3^{{\left({\mathrm{x}}^2-2\right)}^3}\cdot \mathrm{x}{\left({\mathrm{x}}^2-2\right)}^2\cdot \log 3\end{array}$
So, x=0 is a point of local minima and $\mathrm{x}=\sqrt{2}$ is a point of inflection of f.
${\mathrm{f}}^{\prime \prime }\left(\sqrt{2}\right)=0,{\mathrm{f}}^{\prime \prime }\left({\sqrt{2}}^{+}\right)>0,{\mathrm{f}}^{\prime \prime }\left({\sqrt{2}}^{-}\right)<0$
Also,${\mathrm{f}}^{\prime \prime }\left(\mathrm{x}\right)>0\text{ for }\mathrm{x}>\sqrt{2}\text{, so }{\mathrm{f}}^{\mathrm{\prime }}\left(\mathrm{x}\right)$ is increasing.