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Math Help - [SOLVED] Taylor Polynomial approximation

  1. #1
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    [SOLVED] Taylor Polynomial approximation

    What cubic Taylor Polynomial best approximates x^4 + 2x^3 +3x - 3 near x = 2

    take the derivative three times, plug in the value 2 for x in each derivative, divide that by i! ...

    P_3(x) = 35 + 59(x - 2) + 36(x - 2)^2 + 10(x - 2)^3

    Am I correct?
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  2. #2
    Senior Member apcalculus's Avatar
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    Maple says
    10x^3-24x^2+35x-19
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  3. #3
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    Quote Originally Posted by apcalculus View Post
    Maple says
    10x^3-24x^2+35x-19
    I think that maybe expanded and simplified.
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  4. #4
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by diroga View Post
    I think that maybe expanded and simplified.
    Yes 35 + 59(x - 2) + 36(x - 2)^2 + 10(x - 2)^3 and 10x^3-24x^2+35x-19 are equal. According to Mathematica.
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  5. #5
    Senior Member apcalculus's Avatar
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    Wolfram Alpha does a pretty neat job with these kinds of tasks: Type expand 35+ 59(x-2)+ 36(x-2)^2+ 10(x-2)^3 and it spits out the expanded form.

    Direct link:

    http://www76.wolframalpha.com/input/?i=expand+35+%2B+59(x-2)+%2B+36(x-2)^2+%2B+10(x-2)^3
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  6. #6
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by apcalculus View Post
    Wolfram Alpha does a pretty neat job with these kinds of tasks: Type expand 35+ 59(x-2)+ 36(x-2)^2+ 10(x-2)^3 and it spits out the expanded form.

    Direct link:

    http://www76.wolframalpha.com/input/?i=expand+35+%2B+59(x-2)+%2B+36(x-2)^2+%2B+10(x-2)^3
    Thanks. I tried it but instead of typing "Expand" I typed "simplify" and I didn't get anything interesting.
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  7. #7
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    Thanks everybody. Is there a way I can mark this as solved?
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  8. #8
    MHF Contributor arbolis's Avatar
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    Quote Originally Posted by diroga View Post
    Thanks everybody. Is there a way I can mark this as solved?
    Yes. Look at the top of the thread : "Thread Tools", then "Mark this thread as solved".
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  9. #9
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    so thats what that tab is for
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