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Max and Min Values

  1. Nov 16, 2005 #1
    OK, the professor did this problem for us as an example and i got lost somewhere in between. the problem was: find the critical points
    f(x)= x^(4/5)*(x-4)^2

    then he used the product rule to get

    f '(x)= 4/5 x^(-1/5) *(x-4)^2 + x^(4/5) * 2(x-4) = 0

    THEN, the part that threw me off was the next part where he said multiply both sides by 1/5....what did he mean by that? after that you get

    4/5 (x-4)^2 + 2x(x-4) = 0 and so on...

    my question is how and what did he do to get rid of the x^(-1/5) and the x^(4/5)??? :confused:

    Any help would be greatly appreciated
  2. jcsd
  3. Nov 16, 2005 #2


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    Multiply both sides by
  4. Nov 16, 2005 #3


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    He multiplied both sides by [tex]x^{1/5}[/tex], not 1/5.
  5. Nov 16, 2005 #4
    Don't multiply by 1/5, try multiplying by x^(1/5). The whole idea is to turn the exponents into integers, and then you can use the usual methods to find the roots of the equation.
    Last edited: Nov 16, 2005
  6. Nov 16, 2005 #5
    He is not multiplying by 1/5, he is multiplying by x^(1/5). On the zero side, it of course goes away. On the other side, it distributes and x^(1/5)*x^(-1/5)=1 while x^(1/5)*x^(4/5)=x nicely killing off those pesky rational exponents. Good Luck
  7. Nov 16, 2005 #6
    WOOHOOO!!!!! Thanks very much!
  8. Nov 16, 2005 #7


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    "Never seen such unanimity of opinion before in my life"
    Poobah, in "The Mikado"
  9. Nov 17, 2005 #8
    And who said mathmaticians don't have a sense of humor??

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