Questions in differentiation

Select	Question
	$\frac{x}{1+x\,\tan x}$ is maxima at
	If x is real, then greatest and least values of $\frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1}$ are
	The minimum value of $\frac{\log x}{x}$ in the interval $[2,\,\infty )$ is
	The maximum value of ${{x}^{4}}{{e}^{-{{x}^{2}}}}$ is
	If $A+B=\frac{\pi }{2},$ the maximum value of $\cos A\cos B$ is
	The real number x when added to its inverse gives the minimum value of the sum at x equal to
	The denominator of a fraction number is greater than 16 of the square of numerator, then least value of the number is
	The real number which most exceeds its cube is
	The maximum value of $f(x)=\frac{x}{4+x+{{x}^{2}}}$ on $[-1,\,1]$ is
	A cone of maximum volume is inscribed in a given sphere, then ratio of the height of the cone to diameter of the sphere is