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. y = 5 â x2

A(x)=2x(8−x2)=16x−2x3. A'(x)=16−6x2=0⇒x=±√83. There is a maximum at x=√83. So the dimensions that will produce the greatest area are 2×√83 for the base and 513 for the height. The maximum area is 2√83×163≈17.418. enter image source here