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Finding critical numbers of function with rational exponent

  1. May 2, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the critical numbers of the function:

    F(x) = x^(4/5) (x - 4)^(2)

    2. Relevant equations


    3. The attempt at a solution

    I differentiated and got to (1 / 5th root of x) (x - 4)(2x + 4/5(x-4))

    but I dont know how I can simplify the expression to be able to solve for the critical values of x
  2. jcsd
  3. May 2, 2010 #2


    Staff: Mentor

    You're almost there. What values of x make F'(x) = 0? You have three factors, so for F'(x) to be zero, at least one of the factors must be zero.
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