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Critical values

  1. Oct 20, 2009 #1
    f(x) = (1x+10)/(x^2+x+1)

    so the question is to find the critical values for this function

    i know that to find the critical values you have to take the derivative of the function. to do that you have to do the quotient rule

    so you get

    f'(x) = (x^2+x+1)(1)-(1x+10)(2x+1)/(x^2+x+1)^2

    after cleaning it up i got (-x^2-20x-9)/(x^2+x+1)^2

    so you set the numerator equal to 0 and solve it using the quadratic equation so after that you get

    (20 +- sqrt (400 - 36))/-2

    after simplifying i got

    -10 +- sqrt364

    but the website says that is wrong
    where did i go wrong???
  2. jcsd
  3. Oct 20, 2009 #2


    Staff: Mentor

    You forgot to divide sqrt(364) by 2. I get x = -10 +/- sqrt(91)
  4. Oct 20, 2009 #3


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    Your last step should have (1/2)sqrt(364) and can be simplified.
  5. Oct 20, 2009 #4
    how exactly did you get sqrt(91)?
    364 divided by 2 is 182 so where does 91 come from?
  6. Oct 20, 2009 #5


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    [tex] \frac{\sqrt{364}}{2} = \frac{\sqrt{364}}{\sqrt{4}} = \sqrt{ \frac{364}{4}}[/tex]
  7. Oct 20, 2009 #6
    o ok, thanks alot
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