# Second derivative of effective potential

1. Nov 30, 2008

### dswatson

Determine the value of r in terms of l, k, and m for which the following function has a minimum.

V(r) = -(k/r) + (l^2/(2mr^2))

where l, k, and m are positive constants.

Prove that this is a minimum by showing that the second derivative of V(r) at the minimum is positive.

I have no idea how to even begin this...I am horrible at derivatives and am struggling in my physics class with them. Any help would be greatly appreciated.

I am then asked to derive Kepler's third law from Kepler's second law. So I feel I have a lot of work ahead of me.

2. Dec 1, 2008

### malawi_glenn

Then practice derivates!

Try this one:

what is the derivative with respect to x in this function: $$f(x) = x^a$$, where a is a real number, (non zero).

That is all you need for this particlar problem :-)