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Thread: Functions

  1. #1
    Senior Member
    Feb 2008


    $\displaystyle Find\ the\ point\ on\ the\ straight\ line\ 2x+3y=6\ which\ is\ closest\ to\ the\ origin?$

    How would you do this using the principles of continuous functions? I know how to do this by finding the equation perpendicular to the line and then finding the point of intersection.
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  2. #2
    MHF Contributor

    Apr 2005
    What do you mean by "principles of continous functions"? The simplest and best way is to do what you say- find the equation of the perpendicular line.

    Harder would be to write the distance function $\displaystyle \sqrt{x^2+ y^2}= \sqrt{x^2+ (-\frac{2}{3}x+ 2)^2}$ which is minimal only when its square, $\displaystyle x^2+ (-\frac{2}{3}x+ 2)^2$, is minimal, and find where the derivative is 0.
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