Largest Rectangle Possible

[nic_pham]

Find the area of the largest rectangle that has its base on the x-axis and its other two vetices above the x-axis and lying on the parabola y=r-x^2

 

[tkhunny]

Find the vertices

Width = 2*x
Heigth = r - x²

Area = (2*x)*(r - x²) = 2*x*r - 2*x³

Now what?