# Thread: Applications of maxima/minima

1. ## 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...?

2. Hello, ^_^Engineer_Adam^_^!

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".

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!