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Math Help - derivative question

  1. #1
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    derivative question

    Hey

    my question asks: what is the value of the derivative at f(x) = absolute value x when x =0

    Is the answer does not exist because there are no x's left once you do the derivative of /x/ ??? thus the answer is just 1 and cannot be anything else.

    thanks
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  2. #2
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    Krizalid's Avatar
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    Compute \underset{x\to 0}{\mathop{\lim }}\,\frac{f(x)-f(0)}{x-0} then, tell us.
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  3. #3
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    I would appreciate a straight answer instead of replying me with a question........................... (Quit Doing that it's like my third post in a row where I just get a question as a reply)

    F(0) - F(0)/ 0 =

    0/0 --> Correct??

    I don't get what that has to do with my question.!
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  4. #4
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    It has to do with it, if that limit exists, that function should be differentiable at x=0. The limit equals \underset{x\to 0}{\mathop{\lim }}\,\frac{\left| x \right|}{x}, then study \underset{x\to 0^{+}}{\mathop{\lim }}\,\frac{\left| x \right|}{x} and \underset{x\to 0^{-}}{\mathop{\lim }}\,\frac{\left| x \right|}{x}.

    You'll find those limits have different values, thus \underset{x\to 0}{\mathop{\lim }}\,\frac{\left| x \right|}{x} doesn't exist and f is not differentiable at x=0.
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  5. #5
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    oooo ok thanks very much
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