Find the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the parabola. (Round your answers to the nearest hundredth.)

Question

y = 7 - x^2

Answer 1

let P(x,y) be the point in quadrant I lying on the parabola.
Area = 2xy
= 2x(7-x^2)
= 14x - 2x^3
d(Area)/dx = 14 - 6x^2
= 0 for max of area
6x^2 = 14
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take it from there