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

$A$ container is in the shape of an inverted cone. Its height is $6 \ m$ and the radius at the top is $4 \ m$. If it is filled with water at the rate of $3 \ m^3/min$,then the rate of change of the height of the water (in $m/min$) when the water level is $3 \ m$,is

The distance $(s)$ travelled by a particle in time $t$ is given by $s = 4t^2 + 2t + 3$. The velocity of the particle when $t = 3$ seconds is

The displacement $S$ of a moving particle at a time $t$ is given by $S=5+\frac{48}{t}+t^3$. Then its acceleration when the velocity is zero,is

If a particle moves such that the displacement $s$ is proportional to the square of the velocity $v$ acquired,then its acceleration is

$A$ particle moves in a straight line such that its displacement $S$ (in $m$) at a time $t$ (in $sec$) is given by $S(t) = t^3 - 4t^2 + 7t$. The instantaneous velocity $v$ at $t = 4$ is (in $m/sec$)