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Polynomial f(x) word problem help

  1. Sep 22, 2011 #1
    1. The problem statement, all variables and given/known data

    Kaylas lemonade stand has experienced rises /falls in sales caused by temperature changes over 2 summers. Her sales over the first two weeks of summer were tracked according to the model S(x) = x^3 -12x^2 +36x, where x is the number of days and S(x) is the number of sales.

    a) Kayla makes a profit if she sells atleast 10 glasses of lemonade. use the model to determine the number of days that she made profit.

    b) What is the domain/range

    c) describe the weather for the summer in terms of her lemonade sales model. Predict the number of sales on her last sales day (aug31) does this seem reasonable?

    2. Relevant equations

    3. The attempt at a solution

    How do you solve this? Ive tried grouping and factoring but the discriminant is = 0 , IM not sure what to do
    The factor would be (x-6)^2 .

    If you group its x^2-12x +36 which is (x-6) (x-6) . Dont think thats what your supposed to do anyway. Anyone know how to solve?
  2. jcsd
  3. Sep 22, 2011 #2
  4. Sep 22, 2011 #3


    Staff: Mentor

    Have you sketched a graph of this function? In factored form, S(x) = x(x - 6)2. Seeing a graph would help you answer the questions in this problem.
  5. Sep 22, 2011 #4


    User Avatar
    Science Advisor

    You seem to be doing things at random. You have not even stated that "use the model to determine the number of days that she made profit" is the same as solving the inequality
    [itex]S(x) = x^3 -12x^2 +36x\ge 10[/itex]. You are completely ignoring the "at least 10 cups" part.

    Do you understand that "the number of days" must be a positive integer? I see nothing wrong with just plugging positive integers into S(x) and seeing what happens.
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