Finding points farthest away from the origin

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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?
 

Thread 'Finding the nth roots of a complex number'

There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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