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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 -

    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 -

    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?


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