Solve an Ellipse Product Min Problem with LaGrange

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Homework Help Overview

The problem involves using Lagrange multipliers to find points on the ellipse defined by the equation 8x² + 2y² = 16, where the product xy is minimized. The context is within the subject area of optimization in calculus, specifically dealing with constrained optimization problems.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster seeks clarification on the meaning of minimizing the product xy and how it relates to the constraints provided by the ellipse. Participants discuss the nature of the objective function and its relationship to the constraint.

Discussion Status

The discussion is ongoing, with participants exploring the definitions and relationships between the objective function and the constraint. Some guidance has been offered regarding the nature of the objective function and the role of derivatives in finding minima.

Contextual Notes

There is some uncertainty regarding the interpretation of the problem statement, particularly about the conditions for minimizing the product xy and how they relate to the ellipse constraint.

MatSci
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Hello, the problem that i can't figure out says: To Use LaGrange multipliers to find all points on the ellipse 8x^2 + 2y^2 = 16 at which the product xy is a minimum? Any hints appreciated.
 
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What have you done so far?
 
I'm just not sure what the "which the XY product is a minimum" is really asking me.
 
xy is your objective function, the one you're trying to minimize.
 
to have a minimum of a function the 1st derivative must equal 0 and the second derivative must be greater than 0.

does that help?
 
ah ok, and my ellipse is the constraint then?
 
Looks that way.
 

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