- #1

- 68

- 0

## Homework Statement

U = Ax

^{2}- Bx

^{3}

## Homework Equations

du/dx = 2Ax - 3Bx

^{2}

## The Attempt at a Solution

If I was given a potential energy function U = Ax

^{2}- Bx

^{3}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 - 3Bx

^{2}

Now for 2):

Would I set f'(x) = 0 to find the equilibrium points?

f'(x) = 2Ax - 3Bx

^{2}= 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?