A question on weight function from Ashcroft and Mermin book

[mkbh_10]

I am not able to understand the top 2 lines on page 536 that are mentioned regarding the weight function mentioned in chapter 27 of ashcroft and mermin solid state physics book.

I don't get the statement where the authors state Igrad(f)I/f should not be appreciably greater than the minimum value, of order 1/ro ? Why inverse of length is used ?

I know grad(f) gives me the direction of maximum change in f but why has the author used Igrad(f)I/f for a slowly varying function ?

 

[Blackberg]

What chapter-section is that? What edition of the book?