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

$A$ balloon,which always remains spherical,has a variable diameter $\frac{3}{2}(2x+1)$. Find the rate of change of its volume with respect to $x$.

Let $B \equiv (0,3)$ and $C \equiv (4,0)$. The point $A$ is moving on the line $y=2x$ at the rate of $2 \text{ units/second}$. The area of $\triangle ABC$ is increasing at the rate of

The distance $s$ moved by a particle in time $t$ is given by $s = f(t) = t^3 - 6t^2 + 9t$,where $s$ is in metres and $t$ is in seconds. The velocity of the particle at $t = 2 \ s$ is: (in $m/s$)

Two cyclists are moving from a junction of two roads inclined at an angle of $120^{\circ}$ to each other,with velocities of $4 \text{ km/h}$ and $3 \text{ km/h}$ respectively. The rate at which they are separating from each other after $1 \text{ hour}$ is ..... $\text{km/h}$.

For the curve $y=5x-2x^{3}$,if $x$ increases at the rate of $2 \text{ units/sec}$,then how fast is the slope of the curve changing when $x=3$?