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Caclulus Triangle Problem

  1. Dec 19, 2008 #1
    1. The problem statement, all variables and given/known data

    The vertices of a triangle are (0,0), (x, cos x), and (sin3x, 0), where 0 < x < p/2.
    a. If A(x) represents the area of the triangle, write a formula for A(x).
    b. Find the value of x for which A(x) is a maximum. Justify your answer.
    c. What is the maximum area of the triangle?

    2. Relevant equations
    I know this involves min/max problems, and the area of a triangle at some point.

    3. The attempt at a solution
    No idea where to start. I don't see any way to get an area function for the triangle.
     
  2. jcsd
  3. Dec 19, 2008 #2

    HallsofIvy

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    You do know that the area of a triangle if "1/2 base times height", don't you? Draw a picture and see what base and height are for this triangle.
     
  4. Dec 19, 2008 #3
    So is A(x)= (1/2)(sinx)^3(cosx)? If that's true then do I have to take the derivative or something?
     
    Last edited: Dec 19, 2008
  5. Dec 20, 2008 #4
    Is it sin3x or (sinx)^3? Once that is cleared up, how would you usually find the maximum of a function? A derivative would help.
     
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