Find the point on the graph of the function that is closest to the given point. f(x) =  √x, (8, 0) (x, y) =?

Q#3) Find the point on the graph of the function that is closest to the given point.

f(x) =  √x, (8, 0)

(x, y) =?

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    d^2 = (sqrt(x) - 0)^2 + (x - 8)^2

    d^2 = x + x^2 - 16x + 64

    d^2 = x^2 - 15x + 64

    2d * dd/dx = 2x - 15

    2d * 0 = 2x - 15

    0 = 2x - 15

    15 = 2x

    7.5 = x

    f(7.5) =>

    sqrt(7.5) =>

    sqrt(15/2) =>

    sqrt(30/4) =>

    sqrt(30) / 2

    (15/2 , sqrt(30)/2)

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