We are looking to find the point on the cone which is closest to a given point. It needs to be recognized as multivariable that is applied to optimize the problem. We must find the smallest possible distance between the coordinate point and the surface of the cone.
The distance formula is in three variables and will give you the distance between two coordinate points in three-dimensional space.
To optimize the equation, you must eliminate one of the variables and leaving only two variables. This will give a function that can be easily optimized.
Square both sides to simplify the equation. Simplifying gives you the equation you are optimizing.
In order to optimize an equation, you take the partial derivatives of each variable in the equation. The goal to finding partial derivatives is find a critical point.
To find the coordinate point that lies on the surface of the cones, plug in the critical point into the equation. There are two points on the surface of the cone that are equidistant from the given coordinate point.
The second derivative test can be used to determine whether a given coordinate point is a minimum or a maximum on a surface.
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This video tutorial works through math problems/equations that address topics in Calculus 3, Partial Derivatives. This specific tutorial addresses Point on a cone closest to another point.
Length: 9 minutes
Copyright date: ©2013
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