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
|show 2 more comments|
For starter try and see that any rectangle will have first corner at some
Mminimum, ie. zero at