Taylor Polynomials: Why Abs(0) Doesn't Have Center at Xo=0

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The discussion centers on the Taylor polynomials of the function f(x) = |x|, specifically at the point Xo = 0. It is established that the first Taylor polynomial does not exist at this center due to the non-differentiability of f(x) at x = 0. Additionally, the second Taylor polynomial also fails to exist at this point for the same reason, as the derivative of |x| is undefined at x = 0.

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Why does f(x) = abs (0) not have the first Taylor polynomial center at Xo = 0 ?
Does it have second Taylor polynomial center at Xo = 0 ?
 
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ado1lz6 said:
Why does f(x) = abs (0) not have the first Taylor polynomial center at Xo = 0 ?
Does it have second Taylor polynomial center at Xo = 0 ?

What is the derivative of |x| at x= 0?
 
That only explains that f(x) does not have second Taylor polynomial center at Xo=0. What about the first Taylor polynomial ?
Thanks a lot for reply
 

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