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Math Help - Determining the interval on which a function is increasing

  1. #1
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    Determining the interval on which a function is increasing

    I need to determine the interval on whhich f(x) = x - x^(-2) is increasing. I think I should first get the derivative: F' = 1 - (-2x^-3)
    = 1 + 2x^-3
    = 1 + 2/x^3

    I hope I wrote the function = x minus x to the minus 2. I derived 1 + 2 divided by x cubed. Even if I got the derivative right, I do not know how to use this derivative to determine when the function is increasing. Do I make the derivative greater than zero? Please help.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Set the derivative equal to 0 this diveides the x axis inot regions where f ' is always positive or always negative

    then use test points in these regions to determine which.
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  3. #3
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    if you have a graphic calculator you can simply add the formula, I have casio fx-970 and I have a program called graphic function witch can write functions and analyze them.

    My answer from my calculator was
    f(x)=x-x^{-2} is increasing when x\in<-\infty,-1,26><1,\infty>
    The space between is where the function is decreasing

    And then you have to do the same for the derivative and maybe the second derivative. Hope this helps something.
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  4. #4
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    Determining increasing and decreasing intervals of a function

    Senior Member/ Calculus 26. Thatnk you so much for showing me how to determine the increasing interval. I really needed the teaching. I wish you all the best, and will no doubt be asking more questions. Thanks.
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  5. #5
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    Increasing and decreasing intervals

    Thanks hlolli. I purchased a TI-89 Titanium about a month ago. I haven't fully learned how to use it just yet. I am working at it as so my Calculus I course, a little slowly. Thanks

    Quote Originally Posted by hlolli View Post
    if you have a graphic calculator you can simply add the formula, I have casio fx-970 and I have a program called graphic function witch can write functions and analyze them.

    My answer from my calculator was
    f(x)=x-x^{-2} is increasing when x\in<-\infty,-1,26><1,\infty>
    The space between is where the function is decreasing

    And then you have to do the same for the derivative and maybe the second derivative. Hope this helps something.
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