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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...Asked by sonia
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?
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Answered by
Steve
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
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