In the interval $[-2, 4]$,the absolute maximum of $f(x) = 2x^3 - 3x^2 - 12x + 5$ occurs at $x =$

If the petrol burnt in driving a motor boat varies as the cube of the velocity,then the speed (in $km/h$) of the boat relative to the water,going against a water flow of $C \ km/h$,so that the quantity of petrol burnt is minimum,is:

If $ax + \frac{b}{x} \ge c$ for all positive $x$,where $a, b > 0$,then:

Prove that the radius of the right circular cylinder of greatest curved surface area which can be inscribed in a given cone is half of that of the cone.

The height of a right circular cone of maximum volume inscribed in a sphere of diameter $a$ 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