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Math Help - Quadratic Polynomial

  1. #1
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    Quadratic Polynomial

    Let f(x)=ln(1-3x). Find a quadratic polynomial p(x) so that p(0)=f(0), p'(0)=f'(0) and p''(0)=f''(0).

    I don't know how to do this :/
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  2. #2
    Behold, the power of SARDINES!
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    Quote Originally Posted by Velvet Love View Post
    Let f(x)=ln(1-3x). Find a quadratic polynomial p(x) so that p(0)=f(0), p'(0)=f'(0) and p''(0)=f''(0).

    I don't know how to do this :/

    First a quick note if you know how to find a Taylor series centered at x=0 you are done. Just take the first 3 terms.

    So lets suppose you don't so we want a quadratic function

    p(x)=ax^2+bx+c and we want

    f(0)=p(0) \iff ln(1)=c \iff c=0

    So now we have p(x)=ax^2+bx \implies p'(x)=2x+b

    f'(0)=\frac{-3}{1-3(0)}=2(0)+b=p'(0) \implies b=-3

    so now we have p''(x)=2a

    f''(0)=\frac{-9}{(1-3(0))^2}=2a \implies a=-\frac{9}{2}

    So we get

    p(x)=-\frac{9}{2}x^2-3x
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  3. #3
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    Thank you a lot. I've never learned how to do that type of problem. What is that Taylor series?
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