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Math Help - Optimization

  1. #1
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    Optimization

    Find the points on the graph f(x)=2x that is closest to the point (1,0) .

    How would you go about this?
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  2. #2
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    Quote Originally Posted by av8or91 View Post
    Find the points on the graph f(x)=2x that is closest to the point (1,0) .

    How would you go about this?
    The square distance of an arbitary point (x,y) from (1,0) is:

    d^2=(x-1)^2+y^2

    Now substitute from y=2x for either x or y then differentiate and set the derivative to zero, and solve.

    CB
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  3. #3
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    Quote Originally Posted by av8or91 View Post
    Find the points on the graph f(x)=2x that is closest to the point (1,0) .

    How would you go about this?

    A general point on the graph of f(x) is of the form (x,f(x)) , so the distance between such a point and (1,0) is;

    \sqrt{(x-1)^2+(f(x)-0)^2}=\sqrt{x^2-2x+1+4x^2} . Well, do some order here and check this is a function of x so to find is extreme points you have to...

    Tonio
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