U = Ax2 - Bx3
du/dx = 2Ax - 3Bx2
The Attempt at a Solution
If I was given a potential energy function U = Ax2 - Bx3 and am asked to find:
1) The expression for the force as a function of x.
2) The equilibrium points and determine if are they stable or unstable?
So, for 1):
Would I differential the function giving like so?
U' = f'(x) = 2Ax - 3Bx2
Now for 2):
Would I set f'(x) = 0 to find the equilibrium points?
f'(x) = 2Ax - 3Bx2 = 0
In return I get the points of x through the quadratic equation:
x = 0 and X = A/B
If this is all correct how can I determine if a equilibrium point is stable or unstable?