If $f(x) = x^{2}$,find $\frac{f(1.1) - f(1)}{1.1 - 1}$.

The radius of a cylinder is increasing at a rate of $3 \text{ m/s}$ and its height is decreasing at a rate of $4 \text{ m/s}$. Find the rate of change of its volume when the radius is $4 \text{ m}$ and the height is $6 \text{ m}$.

The point on the curve $6y = x^3 + 2$ at which the $y$-coordinate is changing $8$ times as fast as the $x$-coordinate is:

$A$ sphere increases its volume at the rate of $\pi \text{ cm}^3/\text{s}$. The rate at which its surface area increases when the radius is $1 \text{ cm}$ is

$A$ tank in the shape of a rectangular parallelepiped has a volume of $27 \ m^3$. This tank is filled with water such that the rate of change of the water level is thrice the rate of change of the water quantity falling into the tank. The height of the tank (in meters) is:

The rate of change of the surface area of a sphere of radius $r$ when the radius is increasing at the rate of $2 \text{ cm/sec}$ is proportional to