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Math Help - Max Of A Graph

  1. #1
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    Max Of A Graph

    I have an equation:

    y = \frac{1}{\sqrt{1-2x^2+x^4+4x^2z^2}}

    x, y is a variable and z is a constant which we can vary. This equation produces peaks in graphs. I'm asked to find the maximum value of z at which peak will be produced. Which mathematic method would I use? Can I have hints please. Thanks in advance.
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  2. #2
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    I dont see how z can be a constant and a variable. Anyway for finding a maximum you usually differentiate then set the derivative equal to zero and solve that to find maxs and mins. You can use the 2nd derivative to check if it a max or a min found.
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  3. #3
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    z is a constant and when different values are assigned to it, it produces different peaks.

    EDIT: Like a gradient.
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  4. #4
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    Hello,

    As far as I can understand, first find where the peaks occur, and that with respect to z. ( 0=\frac{dy}{dx}=\dots)

    Then find z so that the values of the peaks is maximum.
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