Application of Derivatives

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