$f: R \rightarrow R$ is a function defined by $f(x)=\frac{1}{e^x+2 e^{-x}}$

Assertion (A) : $f(c)=\frac{1}{3}$ for some values of $c \in R$

Reason (R) : $0 < f(x) \leq \frac{1}{2 \sqrt{2}}$ for all $x \in R$

Then, which of the following options is correct?

If the expression $x^3+3 x^2-9 x+\lambda$ is of the form $(x-\alpha)^2(x-\beta)$, then the values of $\lambda$ are

The equation of the normal at $t=\frac{\pi}{2}$ to the curve $x=2 \sin t, y=2 \cos t$ is

If the function $f(x)=\frac{x}{5}+\frac{5}{x},(x \neq 0)$ attains its relative maximum value at $x=\alpha$, then $\sqrt{\alpha^2+2 \alpha-6}=$