The potential energy function of a particle of mass m is V(x) = cx/(x2+a2), where c and a are positive constants.
Qualitatively sketch V as a function of x. Find two equilibrium points: identify which is a position of stable equilibrium, and find the period of small oscillations about it.
The Attempt at a Solution
I think I'm supposed to differentiate and let it equal to zero which gave me:
(c(x2+a2) - 2cx2) / (x2+a2)2 = 0
cx2 + ca2 - 2cx2 = 0
x = a
Putting that into the function gave me: V(x) = cx2/2x2 = c/2
I don't know if any of this is necessary but it doesn't answer the question. Also when it says sketch do I just sub value of x in? Any help would be greatly appreciated.