Variational Calculus: When Is dg(r=r+) ≠ dg(r=r++)?

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Homework Help Overview

The discussion revolves around variational calculus, specifically examining the conditions under which the differential of a function at two distinct points, ##r_+## and ##r_{++}##, are not equal. The original poster presents a scenario where these points yield different function values, prompting questions about the nature of their differentials.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster attempts to compute the differential of the function at one of the points but expresses confusion about the process. Some participants seek clarification on the definitions of the points involved, questioning the assumptions made regarding their relationship.

Discussion Status

The discussion is ongoing, with participants actively seeking definitions and clarifications about the points ##r_+## and ##r_{++}##. There is a focus on understanding the assumptions underlying the problem, but no consensus has been reached yet.

Contextual Notes

Participants note that ##r_{++}## is greater than ##r_+##, indicating a potential misunderstanding of the problem's setup. The original poster has provided limited information, which may affect the clarity of the discussion.

PeteSampras
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Homework Statement



Question:

If ##r_+ \neq r_{++}## and ## g(r=r_+) \neq g(r=r_{++}) ##

When is it fulfilled that ## d g (r=r_+) \neq d g (r=r_+) ## ?

Homework Equations


##r_+ \neq r_{++}##
## g(r=r_+) \neq g(r=r_{++}) ##

The Attempt at a Solution



I tried computing ## dg(r_+) = \frac{\partial g}{\partial r} \Big |_{r=r_+} dr_+##, but i am very confused. This is all the information that i have of this problem.
 
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Can you define #r_{+} , r_{++}## for us? Do it through a forehand or backhand, either is OK ;).
 
WWGD said:
Can you define #r_{+} , r_{++}## for us? Do it through a forehand or backhand, either is OK ;).
I don't understand your assumption. ##r=r_+## and ##r=r_{++}## are two differents points such that ##r_{++}>r_+##
 
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PeteSampras said:
I don't understand your assumption. ##r=r_+## and ##r=r_{++}## are two differents points such that ##r_{++}>r_+##
Sorry, a tennis joke; guess you're tired of them ;).
 

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