The maximum area of a rectangle that can be inscribed in a circle of radius $2 \text{ unit}$ is (in square unit)

An enemy fighter jet is flying along the curve given by $y = x^2 + 2$. $A$ soldier is placed at $(3, 2)$ and wants to shoot down the jet when it is nearest to him. The nearest distance is:

If $\overline{PQ}$ and $\overline{PR}$ are two sides of $\Delta PQR$,for what value of the angle between $\overline{PQ}$ and $\overline{PR}$ is the area of the triangle maximum?

$P$ and $Q$ are two points on a circle with center $C$ and radius $\alpha$. The angle $\angle PCQ = 2\theta$. The radius $r$ of the circle inscribed in the triangle $CPQ$ is maximum when:

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

The absolute maximum value of the function $f(x)=2 x^3-9 x^2+12 x+1$ on the interval $[0,2]$ is: