# calc

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A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 8−x2. What are the dimensions of such a rectangle with the greatest possible area?
width=
length=

• calc -

if the rectangle extends from -x to x,

a = 2xy = 2x(8-x^2)
da/dx = 16 - 6x^2
a has a max at x = 4/√6

width = 8/√3
height = 16/3

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