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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...Asked by Anonymous
A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola
y=11−x^2. What are the dimensions of such a rectangle with the greatest possible area?
y=11−x^2. What are the dimensions of such a rectangle with the greatest possible area?
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Answered by
oobleck
If the base is 2x, then the height is 11-x^2, right? So
A = 2x(11-x^2)
dA/dx = 22-6x^2
so the max area is where x = √(11/3) and y = 22/3
That area is 44/3 √(11/3)
A = 2x(11-x^2)
dA/dx = 22-6x^2
so the max area is where x = √(11/3) and y = 22/3
That area is 44/3 √(11/3)