Finding points farthest away from the origin

[ryan.1015]

Homework Statement

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

Homework Equations

The Attempt at a Solution

 

[Mark44]

What work have you done? The rules of this forum are that you must have at least attempted a solution.

 

[ryan.1015]

well i found the derivative as 18x + 4xy'=4y=12y'=0. is that correct?

 

[Mark44]

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?