Calc

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A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y= 1-x^2. What are the dimensions of such a rectangle with the greatest possible area?

• Calc -

let the point of contact of the top right corner with the parabola be (x,y)
then the base of the rectangle is 2x and its height is y
Area = 2xy
= 2x(1 - x^2)
= 2x - 2x^3

D(area)/dx = 2 = 6x^2
= 0 for a max of area

solve for x , then find y ...
very easy from here on

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