If $f(x) = 2x^3 - 3x^2 - 12x + 5$ and $x \in [-2, 4]$,then the maximum value of the function occurs at which value of $x$?

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

If $m$ and $n$ respectively are the number of local maximum and local minimum points of the function $f(x) = \int_{0}^{x^{2}} \frac{t^{2}-5t+4}{2+e^{t}} dt$,then the ordered pair $(m, n)$ is equal to

Show that of all the rectangles inscribed in a given fixed circle,the square has the maximum area.

If $p(x)$ is a polynomial of degree three that has a local maximum value $8$ at $x=1$ and a local minimum value $4$ at $x=2$,then $p(0)$ is equal to:

$A$ missile is fired from the ground level and rises $x$ meters vertically upwards in $t$ seconds, where $x = 100t - \frac{25}{2}t^2$. The maximum height reached is: (in $\text{ m}$)