The rate of change of the volume of a sphere with respect to its surface area, when its radius is 2 cm , is _________ $\mathrm{cm}^3 / \mathrm{cm}^2$.

Water is being poured at the rate of $36 \mathrm{~m}^3 / \mathrm{min}$ into a cylindrical vessel, whose circular base is of radius 3 meters. Then the water level in the cylinder is rising at the rate of

The equation of the normal to the curve $y=x \log x$ parallel to $2 x-2 y+3=0$ is

If $x=-1$ and $x=2$ are extreme points of $f(x)=\alpha \log |x|+\beta x^2+x$, then