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Math Help - Inequalities/writing set in interval notation

  1. #1
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    Inequalities/writing set in interval notation

    (x-1)^2(x+2)^3\geq 0

    So far I've gathered that the critical numbers are x = 1 and x= -2. I graphed them on the number line. I plugged in test values for each of them.

    When I do that, for every test value I've plugged in they've been \geq 0.

    Now I don't know what that means. Does that mean that since every test proved to be a positive, it'll be the whole thing? [-2, \infty)

    The test intervals were  (-\infty, -2), (-2, 1), (1, \infty).

    I'm also confused on this problem:

    \frac{1}{x} - x > 0

    I already know what it turns into.

    \frac{1-x^2}{x}

    That wasn't the hard part. The hard part is figuring out the critical numbers for this.

    1- x^2

    (1 + x) (1 - x)<br />
    1 -x+x -x^2

    x+1=0
    x = - 1 and x = 1.

    x = 0 is supposed to be a critical number, but I don't know how you get that.
    Last edited by A Beautiful Mind; October 4th 2009 at 06:01 PM.
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  2. #2
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    Yup looks good to me.
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  3. #3
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    Thanks, I updated it with a second problem. I got 2 of the critical numbers. I dunno how you get zero cause in the back of the book it said 0 was a critical number. Only one I'm missing.
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  4. #4
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    Critical numbers are where the either the numerator or the denominator equal 0. So x=0 for this problem sets the denominator to 0 and could possibly change the direction.

    Example: f(x)=1/x

    At x=0 there is obviously an asymptote but the direction of the graph is opposite from each side.
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