If $f: R\to R$ is a differentiable function such that $f^{\text{'}}\left(x\right)>2f\left(x\right)$ for all $x\in R,$ and $f\left(0\right)=1$ then

Let $f:R\to R$ be a continuous function defined by $f\left(x\right)=\frac{1}{e^x+2e^{-x}}$ 

Statement-$1$: $f\left(c\right)=\frac{1}{3}$, for some $c\in R$.

Statement-$2$: $0<f\left(x\right)\le \frac{1}{2\sqrt{2}}$, for all $x\in R$.

The equation of the tangent to the curve $y=x+\frac{4}{x^2}$, that is parallel to the $x$-axis, is

Let $f$ be a function defined by  $f\left(x\right)=\left\{\begin{array}{ll}\frac{\tan x}{x},& x\ne 0\\ 1,& x=0\end{array}\right.$ 

Statement- 1 : $x=0$ is point of minima of $f$ 

Statement- 2 : $f\text{'}\left(0\right)=0.$