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Math Help - derivative question

  1. #1
    Junior Member
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    derivative question

    For the function f(x) = abs value(x^2-3), why is the function not differentiable at x = (3)^.5?

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  2. #2
    Junior Member Evales's Avatar
    Joined
    Oct 2007
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    Re:

    Hey,
    It's not differentiable at 3^0.5 because:
    3^0.5 = x means that
    f(x) = |[(3^0.5)^2]-3|

    [3^0.5]^2 becomes 3^(0.5*2) = 3
    Which means that f(x) = 0
    If we plot the normal x^2 - 3 we find that at y = 0 f(x) crosses the x axis and becomes negative. If we take the absolute value of this we have to flip the graph at this point which means there is a corner at the point x=3
    The limit of the derivative approaching from the left does not equal the limit of the derivative approaching from the right and hence it does not exist.

    Here is a graph of the absolute value function.
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