Arectangle 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?

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Step-by-step explanation:

Given

rectangle with its base on x-axis

and other two corners at parabola

and parabola is downward facing symmetric about y-axis

let y be the y co-ordinate of the corner thus x co-ordinate is given by

Thus lengths of rectangle is & y

Area

differentiating w.r.t to y for maximum area

we get y=

and

A_{max}=16.21 units

i just took the test, the correct answer is .. 31.5 in.