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so when I graph a derivative I know how to use the negative/positive rule according to the slope of the tangent line. But what im really struggling with is the concavity of the derivative graph lines. How do I know which way the derivative graph lines are supposed to face?

As an extended question can you also give me a brief introduction on how to graph the derivative of asymptotes. What must I do different compared to the other graphs.

Thanks so much!

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    right direction2011-09-28

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Calculate the second derivative at the points that the first derivative equals 0. The sign of the second derivative tells you how the first derivative changes and from this you determine the concavity.