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Math Help - optimzation problem #1

  1. #1
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    optimzation problem #1

    Determine the minimal distance from point (-3,3) to the curve given by y=(x-3)^2
    Last edited by mr fantastic; August 12th 2009 at 03:31 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by skeske1234 View Post
    Determine the minimal distance from point (-3,3) to the curve given by y=(x-3)^2
    points are (-3,3) and (x, (x-3)^2)

    use the distance formula
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  3. #3
    MHF Contributor red_dog's Avatar
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    Let [mathA(-3,3), \ P(x,(x-3)^2)[/tex]

    AP^2=(x+3)^2+[(x-3)^2-3]^2=x^4-12x^3+49x^2-66x+45=f(x)

    f'(x)=2(2x^3-18x^2+49x-33)=2(x-1)(2x^2-16x+33)

    f'(x)=0\Rightarrow x=1

    If x<1\Rightarrow f'(x)<0\Rightarrow f decreasing.

    If x>1\Rightarrow f'(x)>0\Rightarrow f increasing.

    Then x=1is a point of minimum. The minimum of f is f(1)=17. The minimum distance is \sqrt{17}
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