Let $M$ and $N$ be the number of points on the curve $y^5-9xy+2x=0$, where the tangents to the curve are parallel to $x$-axis and $y$-axis, respectively. Then the value of $M+N$ equals _______.

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

$P: x=0$ is a point of local minima of $f$

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

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

Let $f:\left(0,1\right)\to \mathrm{ℝ}$ be a function defined by $f\left(x\right)=\frac{1}{1-e^{-x}}$, and $g\left(x\right)=\left(f\left(-x\right)-f\left(x\right)\right)$. Consider two statements

(I) $g$ is an increasing function in $\left(0,1\right)$

(II) $g$ is one-one in $\left(0,1\right)$
Then,