For what values of $x$ does the rate of change of $x^3 - 5x^2 + 5x + 8$ become twice the rate of change of $x$?

Consider a rectangle whose length is increasing at the uniform rate of $2 \, m/sec$,breadth is decreasing at the uniform rate of $3 \, m/sec$ and the area is decreasing at the uniform rate of $5 \, m^2/sec$. If after some time the breadth of the rectangle is $2 \, m$,then the length of the rectangle is ........ $m$.

If water is being poured at the rate of $36 \text{ } m^3/sec$ into a cylindrical vessel with a base radius of $3 \text{ } m$,then the rate at which the water level is rising 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:

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

$A$ 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?