Approximation formula for Higher-order derivative

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Hint: read Section 1.2 of this text.

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Randy Consuegra
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Randy Consuegra

Hi, I'm Computer Science Student. I love maths and I'm from Colombia.

Updated on November 07, 2020

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  • Randy Consuegra
    Randy Consuegra almost 2 years

    I have this assigment

    Derive by using Taylor approximation of $f$ a formula for approximation of $f′(x_0),f′′(x_0),f′′′(x_0),f′′′′(x_0)$ with an error term of order $h^4$.

    I have already done $f′(x_0)$ and $f′′(x_0)$ but I'm stuck trying to get $f'''(x)$. I've done the Taylor expansion for $f(x+h),f(x-h),f(x+2h),f(x-2h),f(x+3h),f(x-3h)$ and don't know what else to do.

    Can someone give me some advice o help me to get $f'''(x)$?

    PD Excuse my bad English.

    EDIT:

    What the assigment want me to get is something like

    $f'''(x)= \frac{-f(x+3h)+8f(x+2h)-13f(x+h)+13f(x-h)-8f(x-2h)+f(x-3h)}{8h^3}+O(h^4)$

  • Randy Consuegra
    Randy Consuegra almost 6 years
    Hi, thnks but I dont get exactly how to get from there to the formula I just added. Sorry for mentioned it just now.
  • Randy Consuegra
    Randy Consuegra almost 6 years
    I was able to solve it, by other methods. But the it was very useful. Thnks.