The stationary points of the curve $y = 8x^2 - x^4 - 4$ are . . . . . .

Given $f(x) = e^{\sin x} + e^{\cos x}$. The global maximum value of $f(x)$

If $p$ and $q$ are respectively the global maximum and global minimum of the function $f(x) = x^2 e^{2x}$ on the interval $[-2, 2]$,then $p e^{-4} + q e^4 =$

Among all sectors of a fixed perimeter,choose the one with maximum area. Then,the angle at the centre of this sector (i.e.,the angle between the bounding radii) is

The maximum area of a triangle whose one vertex is at $(0,0)$ and the other two vertices lie on the curve $y = -2x^2 + 54$ at points $(x, y)$ and $(-x, y)$ where $y > 0$ is:

$P$ 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: