A rectangle is inscribed with its base on the x-axis and its upper corners on th

Question

A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y 6 - x2. What are the dimensions of such a rectangle with the greatest possible area? Width = Height = ). Box 1: Enter your answer as a number (like 5,-3,2.2) or as a calculation (like 5/3,2 3,5+4) Enter DNE for Does Not Exist, oo for Infinity). Box 2: Enter your answer as a number (like 5,-3,2.2) or as a calculation (like 5/3,2 3,5+4) Enter DNE for Does Not Exist, oo for Infinity

Explanation / Answer

Let width = x, height = y A = xy A = x(6-x^2) A = 6x-x^3 dA/dx = 6-3x^2 = 0 =>6 = 3x^2 =>2 = x^2 =>x = sqrt(2) = 1.4142 = width =>y = 6-x^2 = 6-2 = 4 = height

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