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Find the critical numbers

  1. Apr 1, 2013 #1
    1. Find the critical numbers of [itex] F(x) = x^{\frac{4}{5}}(x-4)^{2} [/itex]



    2. Power rule then chain rule



    3. [itex] F'(x) = \frac{4}{5}x^{\frac{-1}{5}} (x-4)^{2}*2(x-4) [/itex] I know two critical numbers are 0 and 4 and I am having problems finding the third one.
     
  2. jcsd
  3. Apr 1, 2013 #2

    Mark44

    Staff: Mentor

    and product rule?
    The first rule to use would be the product rule. It doesn't look to me like you used that rule.
     
  4. Apr 1, 2013 #3

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    Another way to do this is to write
    [tex]F(x)= x^{\frac{4}{5}}(x^2- 8x+ 16)= x^{\frac{14}{5}}- 8x^{\frac{9}{5}}+ 16x^{\frac{4}{5}}[/tex]
     
  5. Apr 1, 2013 #4
    That makes it easier to understand.
     
  6. Apr 1, 2013 #5

    Mark44

    Staff: Mentor

    Yes, but it would also be useful to use the product rule (correctly). The results should be the same for either method, but you might need to use some algebra to confirm that they are the same.
     
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