Posted by **jim** on Tuesday, May 19, 2009 at 8:06pm.

A rectangle has its base on the x-axis and its upper two vertices on the parabola

y=12−x2 .

What is the largest area that the rectangle can have

- calculus -
**Reiny**, Tuesday, May 19, 2009 at 8:16pm
let the points of contact be (x,y) and (-x,y)

so the base is 2x and the height is y

but y=12-x^2

so the

Area = 2xy

= 2x(12-x^2)

= 24x - 2x^3

d(Area)/dx = 24 - 6x^2

= 0 for a max Area

solve 2x^3 - 24 = 0

sub that back into the Area = 2x(12-x^2)

## Answer this Question

## Related Questions

- Calculus - Hello, could someone please help me with this problem? I'm a little ...
- Calculus - Find the dimensions of the rectangle of largest area that has its ...
- derivatives - Applications of derivatives A rectangle has its base on the x axis...
- calculus - A rectangle has its base on the x-axis and its 2 upper corners on the...
- calculus - Find the area of the largest rectangle that has its lower base on the...
- calculus - A rectangle is inscribed with its base on the x-axis and its upper ...
- Calculus - A rectangle is inscribed with its base on the x-axis and its upper ...
- calc - A rectangle is inscribed with its base on the x-axis and its upper ...
- Calculus - A rectangle is inscribed with its base on the x-axis and its upper ...
- Calculus - A rectangle is inscribed with its base on the x -axis and its upper ...

More Related Questions