Finding points farthest away from the origin

In summary, the conversation discusses finding the points on a curve farthest away from the origin by using derivatives. The person asking for help is instructed to use the product rule and chain rule to differentiate the equation and then isolate all terms with the derivative on one side. The conversation also prompts the person to consider how the derivative will help in finding the desired points.
  • #1
ryan.1015
14
0

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

 
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  • #2
What work have you done? The rules of this forum are that you must have at least attempted a solution.
 
  • #3
well i found the derivative as 18x + 4xy'=4y=12y'=0. is that correct?
 
  • #4
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?
 

1. What does it mean to find points farthest away from the origin?

Finding points farthest away from the origin means identifying the points on a graph or coordinate plane that are the greatest distance from the point (0,0), also known as the origin.

2. Why is it important to find points farthest away from the origin?

Finding points farthest away from the origin can be useful in various scientific and mathematical applications. For example, in physics, it can help determine the trajectory of a projectile or the center of mass of an object. In data analysis, it can help identify outliers or extreme values.

3. How do you find points farthest away from the origin?

To find points farthest away from the origin, you can use the distance formula or Pythagorean theorem to calculate the distance between each point and the origin. The point(s) with the greatest distance will be the farthest away.

4. Can points farthest away from the origin be negative?

Yes, points farthest away from the origin can have negative coordinates. This means they are located in the opposite direction from the origin along the x or y axis. For example, a point with coordinates (-5,0) would be the farthest point away on the negative x-axis.

5. Are there any real-life examples of finding points farthest away from the origin?

Yes, there are many real-life examples where finding points farthest away from the origin is important. For instance, in geography, identifying the farthest point from the ocean can help determine the most inland location. In economics, finding the extreme values in a dataset can help identify areas for improvement or potential outliers. Additionally, in navigation, finding the farthest point from a starting location can help determine the most efficient route.

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