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Math Help - Functional Grpahs and optimization

  1. #1
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    Functional Grpahs and optimization

    1.Locate the points on the curve y=x^2 that are closest to the point (0,4.5)?

    2.A rectangle is inscribed in a circle of radius 5m.Determine the maximum possible area for such a rectangle?

    Please provide full steps!
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  2. #2
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    Quote Originally Posted by someone21 View Post
    1.Locate the points on the curve y=x^2 that are closest to the point (0,4.5)?
    We want to minimise a distance, but in practice it's easier to minimise the square of the distance.

    The distance d from a point (x,y) to the point (0,4.5) is given by d^2 = (x-0)^2 + (y-4.5)^2. If the point (x,y) lies on the curve y=x^2 then we can replace x^2 by y, which gives d^2 = y + (y-4.5)^2. Multiply out, complete the square, and you'll find the value of y that minimises d^2.
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