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Numerical Derivatives in Mathematica

  1. Jan 31, 2010 #1
    I have some data in a text file. I want to import this data into Mathematica, and then I want to calculate the numerical derivatives of this data. In particular, I need to find the y value where the first derivative is equal to zero.

    I can import data. I can use the ND function for numerical derivativess, but I'm unsure how to accomplish the rest.

    The data follows a sine curve with increasing amplitude. Do I need to fit the data first somehow?

    Any help is appreciated. I'm kind of a beginner when it comes to Mathematica.
  2. jcsd
  3. Jan 31, 2010 #2


    Staff: Mentor

    I would use an interpolating function. You can take derivatives of interpolated functions which would allow you to simply solve for where they equal 0.
  4. Feb 2, 2010 #3
    Thanks, but I'm having a problem still.

    I have my data imported, and I plotted it using ListPlot. It is a sin like curve with increasing amplitude as the x-values increase.

    I'm thinking that the data is not in the form that InterpolationFunction expects.

    I'm pretty new to mathematica, so any help is appreciated.
  5. Feb 2, 2010 #4


    Staff: Mentor

    Don't use InterpolationFunction, use just Interpolation. It expects the data in the form {{x1,f1},{x2,f2},...} where xi is the ith x-value and fi is the corresponding value f(xi).
  6. Feb 2, 2010 #5
    I tried that one too, but I receive the following error:

    Interpolation::inder :
    The order-2 derivative of {0.08028, 0.01704} is not a tensor of rank 2 with dimensions 2.>>

    I'm not sure what this means. Thanks for your help.
  7. Feb 2, 2010 #6
    Okay, I think I have it working now.

    My data had an extra { at the beginning and the end. Now, when I type

    f = Interpolation[data]

    The output is


    Which I believe is the proper output.

    Now, can I've tried the following code to get the zero values, and I think it is wrong.

    NSolve[f' == 0, x]

    Any help is appreciated. Thanks!
  8. Feb 2, 2010 #7


    Staff: Mentor

    You will want to use FindRoot instead of NSolve, and you need to put in an x before you can solve for it. E.g. f'[x] instead of f'
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