Approximation formula for Higherorder derivative
1,269
Hint: read Section 1.2 of this text.
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Randy Consuegra
Hi, I'm Computer Science Student. I love maths and I'm from Colombia.
Updated on November 07, 2020Comments

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 $f(x+h),f(xh),f(x+2h),f(x2h),f(x+3h),f(x3h)$ 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
$f'''(x)= \frac{f(x+3h)+8f(x+2h)13f(x+h)+13f(xh)8f(x2h)+f(x3h)}{8h^3}+O(h^4)$

Randy Consuegra almost 6 yearsHi, 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 almost 6 yearsI was able to solve it, by other methods. But the it was very useful. Thnks.