# Applications of maxima/minima

• Feb 21st 2007, 04:46 AM
Applications of maxima/minima
a.)Find the area of the largest rectangle having two vertices on the x-axis and two vertices on or above the x - axis and on the parabola y = 9 -x^2

Help What does the two vertices mean in the problem...? :confused:
http://i152.photobucket.com/albums/s...alculus4-1.jpg
• Feb 21st 2007, 05:56 AM
Soroban

Quote:

Find the area of the largest rectangle having two vertices on the x-axis
and two vertices on or above the x-axis and on the parabola: y = 9 -x²

Very confusing . . . then you have a diagram with numbers like "3,0000".

Quote:

What does the two vertices mean in the problem?
You're kidding, right? .Vertices are "corners".
Code:

```                  |                   *               *  |  *           *- - - + - - -*         * :      |      : *         *  :      |      :y *           :      |      :       *---+------+------+---*               x  |  x```
The area of the rectangle is: .A .= .2xy

. . And we know that: .y .= .9 - x²

Therefore, the area function is: .A .= .2x(9 - x²) .= .18x - 2x³

Go for it!