Thread: 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...?

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!