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Homework Help: Optimization calculus problem

  1. Feb 11, 2010 #1
    1. The problem statement, all variables and given/known data
    The illumination of an object by a light source is directly proportional to the strength of the source and inversely proportional to the square of the distance from the source. If two light sources, one three times as strong as the other, are placed 10 feet apart, where should an object be placed on the line between the sources so as to receive the least illumination?

    2. Relevant equations
    1/illumination=distance^2 and illumination=strength. 1/3x=y distance=10 so 1/100= illumination??

    3. The attempt at a solution
    find the derivative of what equation to optimize?
  2. jcsd
  3. Feb 12, 2010 #2


    Staff: Mentor

    Let s = strength of a source
    Let d = distance from source.

    I =ks/d2

    The way I read this is that the total illumination an object receives is the sum of the illuminations from the two light sources, so
    IT = I1 + I2

    From this relationship you should be able to write the total illumination an object at a distance of x feet from the left source gets.

    Then differentiate the expression for IT.
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