A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 7-x^2. What are the dimensions of such a rectangle with the greatest possible area? width=?? height=??

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A rectangle is inscribed with its base on the x-axis and its upper corners on the parabola y = 7-x^2. What are the dimensions of such a rectangle with the greatest possible area?
width=??
height=??

EXPERT ANSWER

area A= 2x(7-x^2) = 14x – 2x^3
dA/dx = 14 – 6x^2 =0.So x = 1.527
width =2x = 3.055m
height = (7-x^2) = 4.668 m
Area max = 3.055*4.668 = 14.2607 m^2