I Differentiation formula: Is this a typo?

[maistral]

TL;DR Summary

Resource found in the 'net, trying to know if this is a typo or not.

Red arrows.

The notes initially say that the error term is positive. After substitution of A and C which are clearly positive, the term suddenly became negative...? Is this a typo, or is there a theory behind this?

 

[anuttarasammyak]

It seems OK observing that the third term of (5.14) is f”(x).

 

[maistral]

It seems OK observing that the third term of (5.14) is f”(x).

What does this imply? That either positive or negative will work?

 

[WWGD]

Summary:: Resource found in the 'net, trying to know if this is a typo or not.

Red arrows.
View attachment 287254

The notes initially say that the error term is positive. After substitution of A and C which are clearly positive, the term suddenly became negative...? Is this a typo, or is there a theory behind this?

It would seem to be the formula for an estimate of the error term in the Taylor series. Is this what your question was?

 

[anuttarasammyak]

Transfer the second term of RHS to LHS.

 

[maistral]

I finally got it! The notation was so confusing, sorry.