Finding points farthest away from the origin

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Homework Help Overview

The problem involves finding points on the curve defined by the equation 9x² + 4xy + 6y² = 11 that are farthest from the origin. The subject area relates to calculus and optimization within the context of implicit differentiation.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the process of finding the derivative of the given equation, with one participant questioning the correctness of their derivative calculation. There is also a focus on the implicit differentiation technique and its application to the problem.

Discussion Status

The discussion is ongoing, with participants exploring the differentiation process and questioning the initial approach taken by the original poster. Guidance has been provided regarding the use of product and chain rules in differentiation, but no consensus has been reached on the correct method or next steps.

Contextual Notes

Participants are navigating the rules of the forum, which require an attempt at a solution before seeking help. There is an emphasis on understanding the implications of the derivative in relation to the problem's goal.

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Homework Statement


find the points on the curve 9x^2 + 4xy +6y^2=11 that are farthest away from the origin


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The Attempt at a Solution

 
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What work have you done? The rules of this forum are that you must have at least attempted a solution.
 
well i found the derivative as 18x + 4xy'=4y=12y'=0. is that correct?
 
ryan.1015 said:
well i found the derivative as 18x + 4xy'=4y=12y'=0. is that correct?
No.
To differentiate the equation you started with, you need to use the product rule and the chain rules.

Why do you have 18x + 4xy', 4y, 12y', and 0 all equal to each other? What you were apparently trying to do was to take the derivative implicitly. When you do that you end up with one equation that involves one or more terms with y' in them. You then isolate all of the terms with y' on one side of the equation, and all other terms on the other side. You then solve for y' using ordinary algebra techniques.

Having said all that, and assuming you can find the derivative, what do you plan to do with it once you have it? How will it help you find what you're looking for in this problem?
 

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