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Math Help - Concavity and Points of Inflection!

  1. #1
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    Concavity and Points of Inflection!

    Have a few questions guys

    1. Test f(x)=5x^4-9x^3+3 for concavity and inflection points.


    **So, to find the inflection points, I know I need to apply the 2nd derivative test which I got: f(x)=60x^2-54x

    From here, I set the 2nd derivative =0 which I am having a hard time with.... I think I need to factor somewhere but I don't see it (well its not obvious to me hence I am here. ) For Concavity, you just plug in numbers that are bigger or smaller than your critical # to find where its concavity correct?


    And can someone help me with the concavity question?

    The Second question:

    2. Test the function 6x^3-(108)x^2+(630)x-2 for relative maximum and minimum.

    ** I applied the second derivative test again to try and find the critical points: f''(x)=24x-216

    Which my textbook tells me is wrong.

    As usual, TIA
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  2. #2
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    For question#1, I think I may have got it...

    So my 2nd derivative was : f''(x)=60x^2-54x

    But I've just noticed I can factor out a 3x so I have now:

    f''(x)= 3x(20x-18)=0
    20x=18
    x=9/10

    So my critical point would be x=9/10?

    Hurrah? Or no Hurrah?
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  3. #3
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    Quote Originally Posted by mvho View Post
    For question#1, I think I may have got it...

    So my 2nd derivative was : f''(x)=60x^2-54x

    But I've just noticed I can factor out a 3x so I have now:

    f''(x)= 3x(20x-18)=0
    20x=18
    x=9/10

    So my critical point would be x=9/10?

    Hurrah? Or no Hurrah?
    you forgot x = 0
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  4. #4
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    Thanks, I'll plug away at the 2nd question now ( looking at it again, I think I need to apply the chain rule somewhere..). I realized that I posted this on the wrong sub forum. Can someone move this to the appropriate forum please?

    Sorry!
    Last edited by mvho; July 5th 2009 at 05:13 PM.
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