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Thread: Help with derivatives and functions!

  1. #1
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    Help with derivatives and functions!

    This is from a question in my textbook:

    "6) Answer each of the following, stating yes or no and a brief explanation: a) Can a figure have a derivative, if it is not a function? Yes/No and explain.
    b) Can a function have a derivative at a point of discontinuity? Yes/No and explain. "

    Thanks for your help!
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  2. #2
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    Re: Help with derivatives and functions!

    Quote Originally Posted by JoshuaJ0 View Post
    This is from a question in my textbook:

    "6) Answer each of the following, stating yes or no and a brief explanation: a) Can a figure have a derivative, if it is not a function? Yes/No and explain.
    b) Can a function have a derivative at a point of discontinuity? Yes/No and explain. "

    Thanks for your help!
    Here's a figure that's not a function. Tangent lines at two points on the figure are drawn at a single value of x. If the derivative existed at this point which one would it be?

    Help with derivatives and functions!-clipboard01.jpg

    A figure could be constructed such that there are infinitely many different values for the derivative at a given point.

    b) This is so fundamental I'm going to have to let you think about it yourself. How would you construct a tangent line to a point of discontinuity? If the limit of the function as x approaches some value doesn't exist can the limit of the difference quotient at that point exist?
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