A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y=1−x 2?
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?
Width =
Height =
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area = 2x(1-x^2) = 2x - 2x^3
derivative is 2 - 6x^2 = 0 at the extrema
x^2 = 1/3
dimensions = 2 / sqrt(3) along x with a y height of 2/3
area = 4 / (3 sqrt(3))