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