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

$A$ ladder of length $10 \ m$ is resting against a vertical wall. The bottom of the ladder is pulled along the ground away from the wall at the rate of $2 \ m/min$. How fast is its height on the wall decreasing when the foot of the ladder is $6 \ m$ away from the wall?

The interval in which the function $f(x) = x^3$ increases less rapidly than $g(x) = 6x^2 + 15x + 5$ is:

If a man of height $1.8 \ m$ is walking away from the foot of a light pole of height $6 \ m$ with a speed of $7 \ km/h$ on a straight horizontal road,then the rate of change of the length of his shadow is (in $km/h$):

The sides of an equilateral triangle are increasing at the rate of $4 \text{ cm/sec}$. Find the rate at which its area is increasing when the side is $14 \text{ cm}$.

The rate of change of volume of a sphere with respect to its surface area when the radius is $4 \text{ cm}$ is