The rate of change of the volume of a sphere with respect to its radius when $r = 7 \ cm$ is . . . . . . .

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:

$A$ particle moves along a straight line according to the law $s = \frac{1}{3} t^3 - 3 t^2 + 9 t + 17$,where $s$ is in metre and $t$ is in second. Its velocity decreases in

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

The volume of a spherical balloon is increasing at the rate of $2 \ cm^3/sec$. When its radius is $4 \ cm$, the rate of change of its surface area (in $cm^2/sec$) is

$A$ point is moving on the curve $y=x^3-3x^2+2x-1$ and the $y$-coordinate of the point is increasing at the rate of $6 \text{ units/sec}$. When the point is at $(2, -1)$,the rate of change of the $x$-coordinate of the point is: