Maximizing the area of a rectangle.

Find the dimensions of the rectangle of the 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=8-x^2.

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...rst let variable x,y
x= length of the base
y= height of the inscribed rectangle.

Now we wish to MAXIMIZE the total AREA of the rectangle
A = (length of base) (height)
A = xy
However, before we differentiate the right-hand side, we have to write it as a function of x only. As we need to have the equation having only one variable, as ...