If $x+y=6, x \geqslant 0, y \geqslant 0$,then the maximum value of $x^2 y$ is

Let $f(x)=4 \cos ^3 x+3 \sqrt{3} \cos ^2 x-10$. The number of points of local maxima of $f$ in the interval $(0, 2 \pi)$ is:

Show that the altitude of the right circular cone of maximum volume that can be inscribed in a sphere of radius $r$ is $\frac{4r}{3}$.

$A$ stone is thrown vertically upwards and the height $x \text{ ft}$ reached by the stone in $t$ seconds is given by $x = 80t - 16t^2$. The stone reaches the maximum height in (in $\text{ s}$)

The function $f(x) = x e^{-x}, \forall x \in R$ attains a maximum value at $x$ equal to:

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