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Math Help - Optimization

  1. #1
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    Optimization

    "for positive constants A and B, the force between 2 atoms in a molecule is given by

    f(r)=-(A/r^2)+(B/r^3)

    where r > 0 is the distance between the atoms. What value of r minimizes the force between the atoms?"

    I can't quite seem to get a grasp on this.
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  2. #2
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    Quote Originally Posted by Nitz456 View Post
    "for positive constants A and B, the force between 2 atoms in a molecule is given by

    f(r)=-(A/r^2)+(B/r^3)

    where r > 0 is the distance between the atoms. What value of r minimizes the force between the atoms?"

    I can't quite seem to get a grasp on this.
    One of those "well-behaved" functions.

    Proceede by taking the derivative and making it zero.

    f'(r)=2A/r^3-3B/r^4
    0=2A/r^3-3B/r^4
    Multiply through by r^4
    Thus,
    0=2Ar-3B
    Thus,
    r=3B/2A, if A\not = 0
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  3. #3
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    Thanks a million sir!
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