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Math Help - Concave, Inflection Points, Etc

  1. #1
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    Concave, Inflection Points, Etc

    Here's the problem:
    [img][/ihttp://img641.imageshack.us/img641/645/screenshot20100321at540.pngmg]

    a. ON what interval(s) is the function concave up?
    b. ON what interval(s) is the function concave down?
    c. FIND all points of inflection (if any).

    So, the first thing I would do is to find the first derivative by doing the whole quotient-rule thing, which gives me:


    The next thing I [think I] have to do is to take the derivative of that (second derivative). After doing the quotient rule of that, I get:


    I'm sort of lost as to what I need to do next. I've been on spring break for a week and have forgotten a lot of this stuff... Looking back at previous problems just seem to confuse me.
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  2. #2
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    Quote Originally Posted by BeSweeet View Post
    Here's the problem:


    a. ON what interval(s) is the function concave up?
    b. ON what interval(s) is the function concave down?
    c. FIND all points of inflection (if any).

    So, the first thing I would do is to find the first derivative by doing the whole quotient-rule thing, which gives me:


    The next thing I [think I] have to do is to take the derivative of that (second derivative). After doing the quotient rule of that, I get:


    I'm sort of lost as to what I need to do next. I've been on spring break for a week and have forgotten a lot of this stuff... Looking back at previous problems just seem to confuse me.
    set g''(x) = 0 ... inflection points on the graph of g(x) occur where g''(x) changes sign.
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  3. #3
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    So it would be + sqrt(3) and - sqrt(3)?
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  4. #4
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    Quote Originally Posted by BeSweeet View Post
    So it would be + sqrt(3) and - sqrt(3)?
    no ... x^2+3 = 0 has no real solutions
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    How do you know that? Sorry for the extremely noob questions...

    So there aren't any inflection points? What about the concavity?
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  6. #6
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    Quote Originally Posted by BeSweeet View Post
    How do you know that? Sorry for the extremely noob questions...

    So there aren't any inflection points? What about the concavity?
    I did not say that ... I just told you that your algebra is wrong.
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  7. #7
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    Hmm...

    So to do this, I set the second derivative to 0, multiply the denominator by both sides, which leaves me with the numerator 6x(x^2+3). I get 0, and +/-sqrt(3), which I guess isn't real, so I just have 0... I'm really not getting any of this stuff, nor do I know what any of this is for.
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  8. #8
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    Quote Originally Posted by BeSweeet View Post
    Hmm...

    So to do this, I set the second derivative to 0, multiply the denominator by both sides, which leaves me with the numerator 6x(x^2+3). I get 0, and +/-sqrt(3).
    x = 0 ... correct

    x = \pm \sqrt{3} is incorrect.

    look and learn ...

    x^2 + 3 = 0

    x^2 = -3

    now you tell me, what number can you put in for x, square, and get -3 ???
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  9. #9
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    Nothing. So the point of inflection is at 0?
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