If $y=7x-x^3$ and $x$ increases at the rate of $4$ units per second, how fast is the slope of the curve changing when $x=2$?

The top of a ladder $6$ metres long is resting against a vertical wall on a level pavement, when the ladder begins to slide outwards. At the moment when the foot of the ladder is $4$ metres from the wall, it is sliding away from the wall at the rate of $0.5 \mathrm{m}/\sec$. How fast is the top-sliding downwards at this instance?

How far is the foot from the wall when it and the top are moving at the same rate?