# Thread: Finding the rectangle of greatest area...

1. ## Finding the rectangle of greatest area...

A rectangle is to be drawn in the first quadrant with one leg on the y-axis, and the other on the x-axis, and a vertex on the curve y = 1-.22x^2 Find the coordinates of that vertex which form the rectangle of greatest area.

2. Originally Posted by derekjonathon
A rectangle is to be drawn in the first quadrant with one leg on the y-axis, and the other on the x-axis, and a vertex on the curve y = 1-.22x^2 Find the coordinates of that vertex which form the rectangle of greatest area.
$\displaystyle A = xy = x(1-.22x^2)$

find $\displaystyle \frac{dA}{dx}$ and maximize

3. ## what do you mean find DA/dx?

do you mean just find the derivative of x(1-.22x^2)?

wouldn't that be (1-.22x^2)*-.44x?

4. Originally Posted by derekjonathon
do you mean just find the derivative of x(1-.22x^2)?

wouldn't that be (1-.22x^2)*-.44x?
no ...

$\displaystyle A = x(1 - .22x^2)$

distribute the x ...

$\displaystyle A = x - .22x^3$

now find the derivative, set it equal to 0, and solve for the value of x that maximizes A.