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Math

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Find the point on the graph of the function that is closest to the given point.

Function Point
f(x) = x^2 (16, 1/2)

(x, y) = ( ) ?

  • Math - ,

    Let D be the distance from a point on the function line from (16, 1/2)

    D^2 = (x-16)^2 + (y - 1/2)^2
    = (x-16)^2 + (x^2 -1/2)^2
    When this is a minimum, dD^2/dx = 0
    2(x-16)+ 2(x^2 -1/2)*2x = 0
    2x - 32 + 4x^3 -2x = 0
    4x^3 = 32
    x = +/- 2
    y = 4

  • Math - ,

    Thanks :)

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