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Math Help - Help, Optimization Math (Taylor series), where is the 1/2?

  1. #1
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    Help, Optimization Math (Taylor series), where is the 1/2?

    Refer to the first few lines of
    Newton's method in optimization - Wikipedia, the free encyclopedia

    giving Taylor expansion approximation

    F(x+DeltaX)=.........+ 1/2 * F2(X) * DeltaX^2




    comes out

    F1(X)+F2(X) * DeltaX = 0




    Why missing the coefficient 1/2 ? is it a mistake?

    thanks.
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  2. #2
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    Quote Originally Posted by jasonHuang View Post
    Refer to the first few lines of
    Newton's method in optimization - Wikipedia, the free encyclopedia

    giving Taylor expansion approximation

    F(x+DeltaX)=.........+ 1/2 * F2(X) * DeltaX^2




    comes out

    F1(X)+F2(X) * DeltaX = 0




    Why missing the coefficient 1/2 ? is it a mistake?

    thanks.
    No mistake. You just said, "F(x+DeltaX)=.........+ 1/2 * F2(X) * DeltaX^2" and f(x+ \Delta x)= f(x)+ f'(x)\Delta x+ (1/2)f"(x)\Delta x^2

    Comparing those second power terms, (1/2)*F2(x)*\Delta x^2= (1/2)f"(x)\Delta x^2. The "1/2" on each side cancels.
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  3. #3
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    now I knew it's take the derivatives of the both side.
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