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Limit Definition of Derivative

  1. Nov 16, 2009 #1
    1. The problem statement, all variables and given/known data
    Use the limit definition of derivative to determine the derivative of the following function:

    f(x) = { sqrt(x^2+1) if x<=0
    0 if x>0

    2. Relevant equations

    I'm not sure as to why the function is not continuous at x=0, and so it's not differentiable at that point.

    3. The attempt at a solution

    The left-hand limit and right-hand limit give me 0. And if I plot a graph, the graph hits 0 as it moves from one function to the other.
     
  2. jcsd
  3. Nov 16, 2009 #2

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    The left hand limit is "1", not "0"! I would think that would be obvious. What is f(-0.001)?
     
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