Let $k$ and $K$ be the minimum and the maximum values of the function $f(x) = \frac{(1 + x)^{0.6}}{1 + x^{0.6}}$ in $[0, 1]$ respectively,then the ordered pair $(k, K)$ is equal to

Find all the points of local maxima and local minima of the function $f$ given by $f(x) = 2x^3 - 6x^2 + 6x + 5$.

If $f(x) = \sqrt{x^2 + x} + \frac{\tan^2 \alpha}{\sqrt{x^2 + x}}$,where $\alpha \in (0, \pi/2)$ and $x > 0$,find the minimum value of $f(x)$.

Let $f, g$ and $h$ be real-valued functions defined on the interval $[0,1]$ by $f(x)=e^{x^2}+e^{-x^2}$,$g(x)=x e^{x^2}+e^{-x^2}$ and $h(x)=x^2 e^{x^2}+e^{-x^2}$. If $a, b$ and $c$ denote,respectively,the absolute maximum of $f, g$ and $h$ on $[0,1]$,then

The minimum value of $\left( x^2 + \frac{250}{x} \right)$ is

The radius of the cylinder of maximum volume,which can be inscribed in a sphere of radius $R$ is :-