I am trying to find the area of the largest rectangle (whose sides are parallel to the coordinate axes) contained in the region bounded by the graphs of $y = 0, y = x^2,$ and $x = 1$ using Mathematica. I am not sure where to begin other than that the area of a rectangle is $l w$. Any ideas?
There are several ways to investigate this problem in Mathematica. The first thing I might do would be to build a
The red rectangle has dimensions
This shows a maximum near 0.66, which suggests the answer might be something like
To confirm this, use
For starter try and see that any rectangle will have first corner at some
Mminimum, ie. zero at