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Math Help - 3rd Degree Taylor Polynomial

  1. #1
    s3a
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    3rd Degree Taylor Polynomial

    Can someone explain to me how to do this problem please?

    Any help would be greatly appreciated!
    Thanks in advance!
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  2. #2
    s3a
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    If it were a problem of the form 1/(1-x) I'd know what to do but it isn't. Any ideas?
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  3. #3
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    This is very peculiar- you use the terms "Taylor Polynomial" and "Taylor Series" but your questions imply that you don't know the definition or formula!

    The "third degree Taylor Polynomial" for function f(x) about x= a is
    \frac{f'''(a)}{3!}(x- a)^3+ \frac{f''(a)}{2!}(x- a)^2+ \frac{f'(a)}{1}x+ f(a).

    Here, f(x)= (7x+ 228)^{5/4}. f(4)= (28+ 228)^{5/4}= 4^5= 1024.

    f'(x)= \frac{5}{4}(7x+ 228)^{1/4}(7)= \frac{35}{4}(7x+ 228)^{1/4} so f'(4)= \frac{35}{4}(28+ 228)^{1/4}= 35.

    Can you get f''(4) and f'''(4)?
    Last edited by HallsofIvy; May 19th 2010 at 04:25 AM.
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  4. #4
    s3a
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    I am VERY confused with this topic. I don't see how f^(n) (a) (x-a)^n /n! relates with taking 3 derivatives of f(x).
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  5. #5
    MHF Contributor

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    Now you've got me confused!

    What do you think " f^{(n)}" means?
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