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Finding largest area

  1. Nov 23, 2008 #1
    1. The problem statement, all variables and given/known data
    find, correct to five decimal places, the dimensions of the rectangle of largest area that has its base on the x-axis and its other two vertices above the x-axis and lying on the curve y=cosx


    2. Relevant equations



    3. The attempt at a solution
     
  2. jcsd
  3. Nov 23, 2008 #2
    this is a standard calc min/max problem. First make an equation of what you want to maximize
    A=bh
    the base is 2 times your x coordinate, and your height is just y so:
    A= 2xy
    now substute in your restraint equation y = cos(x)
    A=2xcos(x)
    now take the derivative with respect to x and set equal to zero. The solution should be the correct x value
     
  4. Nov 23, 2008 #3
    I'm getting a transcendental equation out of this cot(x)=x, guess you have to solve with your calculator from there unless I am making some mistake somewhere, usually these types of problems are a little cleaner to solve.
     
  5. Nov 23, 2008 #4

    Mark44

    Staff: Mentor

    That's what I get, so I think you're on the right track. A trial solution is x = pi/4, for which cot(pi/4) = 1. Those values aren't too far apart. I would keep trying different values, looking for values for which x and cot(x) are closer together, stopping when I get them to agree in 5 decimal places.
     
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