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Help with using the first derivative

  1. Feb 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Use the first derivative to determine where the graph of y = x/(x^2+1) is rising.

    2. Relevant equations



    3. The attempt at a solution

    Ive figured the derivative to be (1-x^2) / (x^2+1)^2 and I know that the derivative > 0 will tell me where the graph is rising. Im just not sure how to figure that out. Do I need to simplify my derivative a bit more to make it work?
     
  2. jcsd
  3. Feb 20, 2009 #2

    Mark44

    Staff: Mentor

    The denominator will always be positive, so all you need to do is determine where the numerator is positive, and where negative. Factor 1 - x^2 and see where it is zero, and where positive, and where negative.
     
  4. Feb 20, 2009 #3
    "Factor 1 - x^2 and see where it is zero, and where positive, and where negative."

    Im not sure I know what you mean here. Factored form it is (x-1)(x+1)

    Its 0 when x = +-1 , positive for 0<x<1 negative for (-infin,0) (1,infin)?
     
  5. Feb 20, 2009 #4

    lanedance

    User Avatar
    Homework Helper

    i think you may have missed the effect of one of the factors...

    you could say (1-x^2) is +ve:
    when
    1-x^2 >0
    implying
    x^2 < 1
     
  6. Feb 21, 2009 #5

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    "Factored form" is NOT (x- 1)(x+ 1), it is (1- x)(1+ x).

    And the graph of y= (1-x)(1+x)= 1- x2, is a parabola opening downward and so y is positive for x between -1 and 1. I don't where you got the "0" in "0< x< 1". Was that a typo?
     
    Last edited: Feb 21, 2009
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