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

$A$ spherical iron ball of radius $10 \, cm$ is coated with a layer of ice of uniform thickness that melts at a rate of $50 \, cm^3/min$. When the thickness of the ice is $5 \, cm$,then the rate at which the thickness (in $cm/min$) of ice decreases is

$A$ spherical iron ball of $10 \text{ cm}$ radius is coated with a layer of ice of uniform thickness that melts at the rate of $50 \text{ cm}^3/\text{min}$. If the thickness of the ice is $5 \text{ cm}$,then the rate at which the thickness of the ice decreases is:

$A$ ladder $5 \ m$ long rests against a vertical wall. If its top slides downwards at the rate of $10 \ cm/sec$,then the foot of the ladder is sliding at the rate of . . . . . . $m/sec$,when it is $4 \ m$ away from the wall.

The rate of change of the volume of a sphere with respect to its surface area,when the radius is $5 \ m$ is

$A$ particle is moving in a straight line. At time $t$,the distance of the particle from its starting point is given by $x = t^3 - 6t^2 + t$. Its acceleration will be zero at