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Math Help - Concavity

  1. #1
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    Concavity

    a)Determine the concavity and points of inflection.
    b) Find the local max and local min points.

    Can someone check my work?

    f(x)=8-x^(1/3)
    f'(x)=-1/(3^(2/3))
    f'(x)= undefined when x=0
    (0,8)

    f''(x)=2/(9x^(5/3))
    f''(x)=undefined when x=0
    (0,8)

    therefore point of inflection occurs at (0,8) and there is no concavity, no local max and min points.

    Question: for this particular case, a vertical tangent, there is no concavity correct??
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  2. #2
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    Quote Originally Posted by skeske1234 View Post



    therefore point of inflection occurs at (0,8) and there is no concavity, no local max and min points.

    Question: for this particular case, a vertical tangent, there is no concavity correct??
    I agree with this

    Quote Originally Posted by skeske1234 View Post

    f(x)=8-x^(1/3)
    f'(x)=-1/(3^(2/3))
    f'(x)= undefined when x=0
    (0,8)

    f''(x)=2/(9x^(5/3))
    f''(x)=undefined when x=0
    (0,8)
    I don't really know what you have done here.
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  3. #3
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    Quote Originally Posted by skeske1234 View Post
    a)Determine the concavity and points of inflection.
    b) Find the local max and local min points.

    Can someone check my work?

    f(x)=8-x^(1/3)
    f'(x)=-1/(3^(2/3))
    f'(x)= undefined when x=0
    (0,8)

    f''(x)=2/(9x^(5/3))
    f''(x)=undefined when x=0
    (0,8)

    therefore point of inflection occurs at (0,8) and there is no concavity, no local max and min points.

    Question: for this particular case, a vertical tangent, there is no concavity correct??

    f''(x) < 0 for x < 0 ... f(x) is concave down on this interval

    f''(x) > 0 for x > 0 ... f(x) is concave up on this interval

    f(x) changes concavity at x = 0, therefore it is a point of inflection.
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  4. #4
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    ok, so let me re-try this:

    a) point of inflection (0,8)
    concave up when x>0
    concave down when x<0

    b) no local max or min points

    is this correct now?

    and another question on a side note: when a function has a vertical tangent, that means that the function can still have concavity, right?
    Last edited by skeske1234; August 20th 2009 at 06:58 PM.
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  5. #5
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    Can someone please answer and verify the above? thanks
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