Posted by **sylvia** on Saturday, November 15, 2008 at 11:02am.

A rectangle is to be inscribed under the arch of the curve y=4cos(.5x) from x=-pi to x=pi. What are the dimensions of the rectanlge with the largest area and what is the largest area? please explain.

- calculus -
**drwls**, Saturday, November 15, 2008 at 11:45am
The curve describes the arch of a cosine function that goes from 0 at x = pi, to 1 at x = 0, and back down to 0 at x = pi. Pick two points on that curve, at x = + and - a, to construct an inscribed rectangle. The dimensions of the rectangle will be width = 2a and height = 4 cos (a/2).

The area will be A(a)= 8 a cos (a/2).

Find the value of a that maximizes this area

dA/da = 0

8 cos (a/2) -8a sin (a/2) = 0

a = cot (a/2)

That will have to be solved by iteration or graphing. I get a = 1.306

## Answer This Question

## Related Questions

- Calculus - Hello, could someone please help me with this problem? I'm a little ...
- Calculus - I have to find the area of the largest possible rectangle that can be...
- Calculus - 3) Consider rectangles located as shown in the first quadrant and ...
- calculus - A rectangle with its base on the x-axis is to be inscribed under the ...
- Calculus - Show that the rectangle with the largest area that is inscribed ...
- calculus - A rectangle with its base on the x-axis is to be inscribed under the ...
- Calc - Find the area of the largest rectangle that can be inscribed under the ...
- calculus - Find the dimensions of the rectangle with the largest area that is ...
- Math - The first question is this: Helen designs a rectangle with an area of 225...
- calculus - Find the area and dimensions of the largest rectangle (with sides ...

More Related Questions