## Essential University Physics: Volume 1 (4th Edition)

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.