Find the points on the surface closest to the origin

Click For Summary

Homework Help Overview

The problem involves finding the points on the surface defined by the equation z² = xy + 4 that are closest to the origin. The context is within multivariable calculus, specifically focusing on optimization techniques.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss using the distance formula and mention the potential application of Lagrange multipliers for optimization. There are inquiries about the details of these methods and the challenges faced in applying them.

Discussion Status

The discussion is ongoing, with participants sharing suggestions on how to approach the problem. Some guidance has been provided regarding the formulation of the distance function and the use of constraints, but there is no explicit consensus on the best method yet.

Contextual Notes

There are indications of uncertainty regarding the application of Lagrange multipliers, and participants are encouraged to seek additional resources for clarification. The original poster expresses difficulty with the distance formula, suggesting a need for further exploration of the problem setup.

EgyptMind
Messages
3
Reaction score
0
1. Homework Statement
find the points on the surface z^2=xy+4 closest to the origin

i tried the distance formula but it got too messy, i think there's an approach using lagrange multiplier but i just can't quiet figure it out...?
 
Last edited:
Physics news on Phys.org
to use lagrange, write the function you are trying to minimise (distance to origin r^2 = x^2 + y^2 + z^2), and use the surface as the constraint
 
a little more details...?
 
what have you tried? post #2 outlines a method to attempt
 
if you;re not sure about lagrange multipliers, try a google search, i found
http://www.uAlberta.ca/MATH/gauss/fcm/calculus/multvrbl/basic/Extrema/Lgrng_mltplrs_exmpl.htm
 
Last edited by a moderator:
EgyptMind said:
1. Homework Statement
find the points on the surface z^2=xy+4 closest to the origin

i tried the distance formula but it got too messy, i think there's an approach using lagrange multiplier but i just can't quiet figure it out...?
What did you try? If you use lanedance's suggestion, to minimize x^2+ y^2+ z^2 rather than \sqrt{x^2+ y^2+ z^2} (whatever minimizes one minimizes the other) it should not be "too messy".
 

Similar threads

Replies
3
Views
10K
  • · Replies 5 ·
Replies
5
Views
2K
  • · Replies 9 ·
Replies
9
Views
4K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
1
Views
2K
  • · Replies 8 ·
Replies
8
Views
2K
  • · Replies 7 ·
Replies
7
Views
2K
  • · Replies 3 ·
Replies
3
Views
3K
Replies
4
Views
2K
  • · Replies 4 ·
Replies
4
Views
25K