calculus - applied problems

Max area - A Norman window is constructed by adjoining a semicircle to the top of an ordinary rectangular window. Find the dimensions of a Norman window of maximum area if the total perimeter is 16 feet.
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  1. let the radius of the circle be x ft
    then the base of the rectangle is 2x ft
    let the height of the rectangle be y ft

    2x + 2y + pi x = 16
    y = (16-2x- pix)/2

    Area = pi x^2/2 + 2xy
    = pi x^2/2 + 2x(16-2x-pix)/2
    = pi x^2/2 + 16 - 2x - pix

    d(Area)/dx = pix - 2 - pi
    = 0 for a max of area.

    etc.

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  2. My anus is leaking acid.

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