If a spherical balloon has a variable diameter $3x + \frac{9}{2}$,then find the rate of change of its volume with respect to $x$.

The displacement of a particle at the time $t$ is given by $s = \sqrt{1+t}$. Then its acceleration $a$ is proportional to:

At present,a firm is manufacturing $2000$ items. It is estimated that the rate of change of production $P$ with respect to the additional number of workers $x$ is given by $\frac{dP}{dx} = 100 - 12\sqrt{x}$. If the firm employs $25$ more workers,then the new level of production of items is:

$A$ point is moving along the curve $y^3 = 27x$. The interval in which the abscissa changes at a slower rate than the ordinate is

The distance $s$ in meters covered by a particle in $t$ seconds is given by $s = 2 + 27t - t^3$. The particle will stop after covering a distance of:

If the rate of increase of the area of a circle is not constant but the rate of increase of the perimeter is constant,then the rate of increase of the area varies: