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?

Question

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?

Answer 1

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.

Answer 2

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