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Second derivative of effective potential

  1. Nov 30, 2008 #1
    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. jcsd
  3. Dec 1, 2008 #2


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    Science Advisor
    Homework Helper

    Then practice derivates!

    Try this one:

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

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