Maximum Area of Rectangle Between Parabola and x Axis

What is the maximum area of a rectangle enclosed between the parabola  
  and the  
From the diagram, the base of the rectangle is  
  and the height is  
  os the area is  
  and solve to give  
\[x= \frac{4 \sqrt{3}}{3}\]
The area is then  
\[A=16 \frac{4 \sqrt{3}}{3} - (\frac{4 \sqrt{3}}{3})^3= \frac{128 \sqrt{3}}{9}\]

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