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ryan.1015
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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
No.ryan.1015 said:well i found the derivative as 18x + 4xy'=4y=12y'=0. is that correct?
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.
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.
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.
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.
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.