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

1. 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.

2. Originally Posted by jasonHuang
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 $\displaystyle f(x+ \Delta x)= f(x)+ f'(x)\Delta x+ (1/2)f"(x)\Delta x^2$

Comparing those second power terms, $\displaystyle (1/2)*F2(x)*\Delta x^2= (1/2)f"(x)\Delta x^2$. The "1/2" on each side cancels.

3. now I knew it's take the derivatives of the both side.