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Math Help - Open Interval differention

  1. #16
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    Re: Open Interval differention

    Quote Originally Posted by rgjf1307 View Post
    The format Plato used earlier is along the lines of what I was hoping to achieve, I was just wondering how, using the same notation, would you define a critical point of a differentiable function?
    A function has a critical point if its derivative fails to exist at the point or if its derivative is zero at that point.

    If a function f is not continuous at x_0 then it has no derivative at x_0 so that is a critical value.

    On the other hand, the slope on the left at x_0 may not be the slope on the right at x_0, in that case we call that a "spike". There is no derivative there.
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  2. #17
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    Re: Open Interval differention

    You say you're taking a calculus course and you refer to a text, but haven't seen a definition of "derivative"? Before you report your instructor, you should make absolutely sure that you're right. I'm not saying you're lying, but rather that you missed the definition in the book. Even though that seems unlikely, a calculus book not having a definition of derivative seems even less likely.

    Wikipedia is also helpful for basic definitions like this.
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