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Find derivative where f(x) has three products

  1. Oct 14, 2012 #1
    1. The problem statement, all variables and given/known data

    Trying to find all Max and Min.

    F(x) = x^(2/3)(x^2 - 4)

    2. Relevant equations
    I know to use the product rule

    3. The attempt at a solution

    I tried and got this answer:

    x^(10/3) + (2(x+2)(x-2)) / 3x^(1/3)
     
  2. jcsd
  3. Oct 14, 2012 #2
    You could also just multiple the x^2/3 through so that you don't have to bother with the product rule.
     
  4. Oct 14, 2012 #3
    Thanks a lot! I got (8(x+1)(x-1)) / (3x^(1/3)) which is the right answer.
     
  5. Oct 14, 2012 #4
    Using the product rule gives
    [itex]\frac{2}{3}[/itex]x[itex]^{-1/3}[/itex]*(x[itex]^{2}[/itex]-4) + 2*x[itex]^{5/3}[/itex]

    modifying this gives (try it):
    x[itex]^{-1/3}[/itex]*([itex]\frac{8}{3}[/itex]x[itex]^{2}[/itex] - [itex]\frac{8}{3}[/itex])

    For min/max equal both factors of this equation to 0 and off course check the domain. Does the expression exist at min/max?
     
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