The minimum value of $f(x) = x + \frac{4}{x + 2}$ for $x > -2$ is

The number of critical points of the function $f(x)=(x-2)^{2/3}(2x+1)$ is:

Let $AD$ and $BC$ be two vertical poles at $A$ and $B$ respectively on a horizontal ground. If $AD = 8 \ m$,$BC = 11 \ m$ and $AB = 10 \ m$,then the distance (in meters) of point $M$ on $AB$ from the point $A$ such that $MD^2 + MC^2$ is minimum,is

The curve $f(x) = e^x \sin x$ is defined in the interval $[0, 2 \pi]$. The value of $x$ for which the slope of the tangent drawn to the curve at $x$ is maximum,is

The local maximum value $l$ and local minimum value $m$ of $f(x) = \frac{x^2+2x+2}{x+1}$ in $R - \{-1\}$ exist at $\alpha, \beta$ respectively,then $\frac{l+m}{\alpha+\beta} =$

In $\triangle ABC$,$\angle B=90^{\circ}$ and $(b+a)$ is always a constant. In order that $\triangle ABC$ encloses the maximum area,$\angle C=$