Results 1 to 2 of 2

Math Help - Finding the Minimum (Word Problem)

  1. #1
    Member
    Joined
    Jul 2007
    Posts
    75

    Question Finding the Minimum (Word Problem)

    A smokestack deposits soot on the ground with a concentration inversely proportional to the square of the distance from the stack. With two smokestacks d miles apart, the concentration of the combined deposits on the line joining them, at a distance x from one stack, is given by S=c/(x^2)+k/((d−x)^2)
    where c and k are positive constants which depend on the quantity of smoke each stack is emitting. If k=2c, find the point on the line joining the stacks where the concentration of the deposit is a minimum.

    I plugged in 2c for k and then differentiated to get:
    S'=(-4c)/((x-d)^3)-(2y)/(x^3)
    Then I figured that I should set it equal to zero and solve for x, which I tried to do but did so incorrectly.

    Can someone give me a hand? Am I going about this the right way? Did I make a mistake when I took the derivative? Should I be setting the derivative equal to zero and solving for x? What should x be then?
    Thanks!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Eater of Worlds
    galactus's Avatar
    Joined
    Jul 2006
    From
    Chaneysville, PA
    Posts
    3,001
    Thanks
    1
    See this example. Very similar. Scroll down to #3.

    http://www2.kpr.edu.on.ca/cdciw/math...ex/210-216.pdf
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Minimum/Maximum Word Problem
    Posted in the Calculus Forum
    Replies: 0
    Last Post: September 6th 2011, 12:07 PM
  2. Minimum Cost Word Problem
    Posted in the Calculus Forum
    Replies: 8
    Last Post: April 1st 2009, 04:56 PM
  3. Replies: 1
    Last Post: November 2nd 2008, 05:28 PM
  4. Replies: 2
    Last Post: November 11th 2007, 09:15 AM
  5. word problem minimum distance
    Posted in the Calculus Forum
    Replies: 1
    Last Post: January 5th 2007, 10:29 AM

Search Tags


/mathhelpforum @mathhelpforum