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Math Help - 2nd Derivative Chart

  1. #1
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    2nd Derivative Chart

    2nd Derivative Chart-2nd-derivative-graph.jpg

    Where (what interval) on f is the graph concave up?

    This IS the graph of the 2nd derivative. So to answer this question, perhaps we need the graph of the function. So do we take the 2nd integral and graph?

    Answer: (-1, 3) why?
    Last edited by Jason76; August 26th 2013 at 06:00 PM.
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  2. #2
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    Re: 2nd Derivative Chart

    Hey Jason76.

    Hint: The definition of concave up is when d^2y/dx^2 > 0. From here:

    Second derivative test - Wikipedia, the free encyclopedia
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    Re: 2nd Derivative Chart

    Quote Originally Posted by chiro View Post
    Hey Jason76.

    Hint: The definition of concave up is when d^2y/dx^2 > 0. From here:

    Second derivative test - Wikipedia, the free encyclopedia
    How does that relate to the shown graph, which is concave down?
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  4. #4
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    Re: 2nd Derivative Chart

    You said in your original post that the function was concave up.

    Remember you are talking about the sign of the second derivative (and your graph is of the second derivative not the actual function).
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  5. #5
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    Re: 2nd Derivative Chart

    Quote Originally Posted by chiro View Post
    You said in your original post that the function was concave up.

    Remember you are talking about the sign of the second derivative (and your graph is of the second derivative not the actual function).
    So if the original graph is concave up, then the 2nd derivative is concave down. Why?

    Actually, what I'm trying to say: If the 2nd derivative is concave down, then HOW do we know the original one was concave up??
    Last edited by Jason76; August 26th 2013 at 08:06 PM.
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  6. #6
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    Re: 2nd Derivative Chart

    You are looking at the sign of the second derivative at a point (or an interval as you are doing).

    Don't look at the concavity of the 2nd derivative: just look at the sign of the derivative.

    Also note that a function can have segments that are both concave up and concave down in different regions.
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