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Math Help - Please help me with something my teacher didn't teach us

  1. #1
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    Please help me with something my teacher didn't teach us

    How do you do this problem?

    Which points on the graph of y=4-(x^2) are closest to the points (0,2)?
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by PrincessIsrael View Post
    How do you do this problem?

    Which points on the graph of y=4-(x^2) are closest to the points (0,2)?
    Employ the distance formula.
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  3. #3
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    Welcome to the Math Help Forum!

    To find the point on y=4-x^2 closest to (0,2), we first do as VonNemo said and use the distance formula to obtain a function of the distance s from a point on the curve to (0,2) as a function of x:

    s=\sqrt{(x-0)^2+((4-x^2)-2)^2}=\sqrt{x^2+(2-x^2)^2}.

    We now find the value of x for which s is a minimum. To do this, we differentiate s and find all critical points. As s is differentiable everywhere and has no boundary points, the only critical points will be those at which s'=0. As s approaches infinity in both directions of the x-axis, at one of these critical points we must find our minimum.

    Hope this helps!
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