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.© SolutionLibrary Inc. solutionlibary.com 9836dcf9d7 https://solutionlibrary.com/math/calculus-and-analysis/maximizing-the-area-of-a-rectangle-27c
...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 ...