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Math Help - Some true of false statements(Check my answers)

  1. #1
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    Some true of false statements(Check my answers)

    A.) If f(x) is locally linear at x = 5, then f(x) is definately differentiable at x = 5. False
    B.) If g(x) has a point of discontinuity at x = 2, then f '(2) cannot possibly exist. True

    I'm pretty sure I am right, but I'm never too sure. Could you please explain why the answers are what they are? Thanks.
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  2. #2
    Junior Member woof's Avatar
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    you almost have it

    Locally linear, intuitively, means that, near 5, the function looks like a line, and, in fact, the tangent line exists there....the only tricky part is when the tangent line is vertical. Then the function looks like a line locally, but the derivative does not exist (since a vertical tangent has an undefined slope). Thus, the answer to the first question is false.

    In order for a function to be differentiable at a point, it must be continuous there. Thus, if a function is not continuous at a point, it's derivative there cannot exist, and the second question is true.
    Last edited by woof; November 8th 2010 at 02:53 AM. Reason: added info
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