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Optimazation Problem

  1. Nov 19, 2007 #1
    Hi! I have a tricky optimization question here. Not so much setting it up, but solving the derivative for x. (if i did set it up right)

    Question: A what angle of theta is the trough (trapezoidal prism) to allow maximum volume?
    Unfortunately, i don't have any program that allows me to draw out the diagram (not even paint) so hopefully my symbols/letters diagram will substitute

    Face of prism, prism is 20m in length
    \ |____| /

    the shorter base (b1) is 1m, while the hypotenuse of the end triangles are 1m as well
    height is assigned as x while the shorter side of the triangle is (1-x^2)^(1/2)
    (the longer base) b2=1+2(1-x^2)^(1/2 theta is the angle between x and the hypotenuse which i know can be solved by cos(theta)=x

    so: V=lh (b1+b2)
    therefore: V=20x(2+2(1-x^2)^(1/2))/2

    0= -40x^2+20(1-x^2)^(1-2)+20

    IF i did everything correctly, my question is, how would I solve for x with the root (1-x^2) in the way? I tried squaring all terms, bu that only left me with X^4 and X^2.

    help appreciated! thanks.
    Last edited: Nov 19, 2007
  2. jcsd
  3. Nov 19, 2007 #2


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