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

[ado1lz6]

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 ?

 

[HallsofIvy]

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?

 

[ado1lz6]

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