Posted by **Micah** on Sunday, July 11, 2010 at 10:45pm.

What is the largest rectangle that can be inscribed in the first quadrant of the ellipse 9x^2+16y^2=144?

- Calculus -
**Reiny**, Monday, July 12, 2010 at 7:09am
base along x-axis, height along y-axis, bottom left vertex at (0,0).

let the top right vertex be (x,y)

from equation

y = (1/4)√(144 - 9x^2)

Area = xy

= x(1/4)√(144 - 9x^2)

differentiate using the product rule, set the derivative equal to zero and solve for x

I got x = 4√3/3 for a max area of 384√3/3

but check my arithmetic.

## Answer this Question

## Related Questions

CIT - find the dimension of the largest triangle that can be inscribe in the ...

Calculus - I have to find the area of the largest possible rectangle that can be...

math - A rectangle with sides parallel to the coordinate axes is inscribed in ...

Calculus - SOS...help!!! please email me at 969e221 at g mail. com here is the ...

Calculus - 3) Consider rectangles located as shown in the first quadrant and ...

Calculus - A rectangle in the first quadrant has one vertex as the origin, and ...

Calculus - A rectangle in the first quadrant has one vertex as the origin, and ...

calculus - find the dimensions of the rectangle of maximum area that can be ...

Calculus - Hello, could someone please help me with this problem? I'm a little ...

calculus - A rectangle is to be inscribed under the arch of the curve y=4cos(.5x...