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Am looking for minimum

  1. Jul 12, 2004 #1
    I have
    i=1 to 3

    I need such N that gives minimum for f(N)?
    Last edited: Jul 12, 2004
  2. jcsd
  3. Jul 12, 2004 #2


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    [tex]f(N) = \sqrt{\sum _{i=1} ^3 \left (\frac{A_i}{1 - N} + \frac{B_i}{N} \right )^2 }[/tex]


    [tex]\frac{d}{dN} \left [ \sum_i g_i(N) \right ] = \sum g_i'(N)[/tex]

    Why is this true? Observe:

    [tex]\frac{d}{dN} \left [ \sum _i g_i(N) \right ] = \frac{d}{dN}[g_1(N) + g_2(N) + g_3(N)][/tex]

    [tex]\ = g_1'(N) + g_2'(N) + g_3'(N) = \sum g_i'(N)[/tex]

    Note, [itex]g_i(N) = \left ( \frac{A_i}{1 - N} + \frac{B_i}{N} \right )^2[/itex] and [itex]\sum _i[/itex] is just a shorthand way of saying [itex]\sum _{i = 1} ^3[/itex].

    Now, f(N) reaches a minimum where f'(N) is zero or undefined. I've given you a way to easily find the derivative for f(N). You can tell where it will be zero or undefined. Take all those critical values for N where f'(N) is zero or undefined, plug those values of N into f(N), and choose the least value.
  4. Aug 26, 2004 #3


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    It looks like AKG forgot to take the square root into account, but consider that when f is a minimum, f^2 is a minimum if f > 0, or a maximum if f < 0.
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