Calculus I

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  • #13241

    Ezra Halleck
    Participant

    Which of the following functions is (are) continuous at but not differentiable there? Why?

    This problem requires that you use your calculator to graph the given functions. To be continuous, informally, it means you can graph them without lifting up your pencil. To be differentiable is roughly equivalent to being “smooth” (no sharp corners). However, if the function has a vertical tangent line, this also not allowed even if the function is “smooth”.

    #16867

    Ezra Halleck
    Participant

    not differentiable means either a corner exists (not smooth) or a vertical tangent line.
    A) is smooth at and has a hor tang line so it is differentiable
    B) x^4/3 is similar to A)
    C) has vertical tangent line so is not differentiable
    D) also has vertical tangent line

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