Posted by **kelli** on Wednesday, December 9, 2009 at 8:07pm.

a rectangle is to be inscribed under the arch of the curve y = 2cosx from x=-pi to x=pi. What is the length of the base of the rectangle with maximum area?

can someone help me with this....i have a lot of problems to do just like this but i don't understand them. can someone show me how to do this problem step by step, please?

- math -
**bobpursley**, Wednesday, December 9, 2009 at 8:21pm
Area= width*height

Lets just do one side.

area= x*2cosX

darea/dx= 2x*2cosx- 2x^2sinx=0

4xcosx=2x^2 sinX

2= x tanx

I get a graphical solution very near PI/3, -PI/3, so sthe base is 2PI/3

I cant find an exact solution. Check my work.

- math -
**kelli**, Wednesday, December 9, 2009 at 8:26pm
my teacher taught me how to do it like this but i cant seem to get an answer.

try to follow my work and please help

so the area for both sides is:

A= 2x(2cosx)

then i have to find the deriviative, which is:

a= 4cosx-4xsinx (is this deriviative right?)

then i have to set it equal to zero and solve but this is where i get stuck. can you help me with this part?

4cosx-4xsinx=0

## Answer This Question

## Related Questions

- math - a rectangle is to be inscribed under the arch of the curve y = 2cosx from...
- calculus - A rectangle is to be inscribed under the arch of the curve y=4cos(.5x...
- calculus - A rectangle with its base on the x-axis is to be inscribed under the ...
- math analysis - A rectangle with its base on the x axis is to be inscribed under...
- Math - A rectangle is inscribed in a semi circle of radius 2, let x represent ...
- calculus - A rectangle with its base on the x-axis is to be inscribed under the ...
- math - an isolation triangle has a base of 6 units and a height of 12 units. ...
- Math - A rectangle is inscribed in a circle of radius r. If the rectangle has ...
- Precalculus - The sides of an isosceles triangle are 10 cm, 10 cm, and 12 cm. A ...
- geometry - The height of triangle ACE is 12 and base AE=20. A rectangle is ...

More Related Questions