The volume of a sphere is increasing at the rate of $4 \pi \text{ cm}^3/\text{sec}$. When its volume is $288 \pi \text{ cm}^3$, the rate of increase (in $\text{cm/sec}$) in its radius is

For the curve $y=5x-2x^{3}$,if $x$ increases at the rate of $2 \text{ units/sec}$,then how fast is the slope of the curve changing when $x=3$?

$A$ stone thrown vertically upwards has its motion described by the equation $s = 13.8t - 4.9t^2$,where $s$ is in meters and $t$ is in seconds. The velocity at $t = 1$ second will be ...... $m/s$.

$A$ street light is at the top of a $12 \ m$ pole. $A$ man $2 \ m$ tall walks away from the pole towards a wall $12 \ m$ away from the pole at a speed of $1/2 \ m/s$. The rate at which his shadow on the wall is decreasing when he is $8 \ m$ from the wall is:

If $f(x) = 2x^{2}$,find $\frac{f(3.8) - f(4)}{3.8 - 4}$.

The height of a cone with semi-vertical angle $\pi / 3$ is increasing at the rate of $2 \text{ units/min}$. The rate at which the radius of the cone is to be decreased so as to have a fixed volume always is