Answer
a) 47 meters
b) Unstable
Work Step by Step
a) We know that at this point, the value of the force, which equals $\frac{dU}{dx}$, must be 0. Thus, we find:
$U=mg(.94x-.01x^2) \\ \frac{dU}{dx}=mg(.94-.02x) \\ 0 = mg(.94-.02x)\\x =\fbox{47 meters}$
b) We take the second derivative to find:
$ \frac{d^2U}{dx^2}=-.02$
Since this is less than 0, the equilibrium is unstable.
