find the largest area of a rectangle with one vertex at the parabola y=9-x^2, another at the origin, and the remaining two on the positive x-axis and positive y-axis respectively

Answer 1

Area = xy where y=9-x²

A = 9x-x³

dA/dx = 9-3x²

The derivative is 0 when x=√3

And the area is maximized when x √3 and y = 6