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Thread: Is the function f(x) differentiable?

  1. #1
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    Post Is the function f(x) differentiable?



    Please explain.
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  2. #2
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    Do you know the sufficient and necessary conditions for a function to be differentiable?
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  3. #3
    Behold, the power of SARDINES!
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    Quote Originally Posted by acarril2 View Post


    Please explain.
    Use first principles e.g

    $\displaystyle \displaystyle \lim_{x \to 0}\frac{f(x)-f(0)}{x-0}$

    Hint: the squeeze theorem will be helpful.
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  4. #4
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    1) Use the usual rules of differentiation to find the derivative for x NOT equal to 0.

    2) Use $\displaystyle \lim_{h\to 0} \frac{f(h)- f(0)}{h}$ to find the derivative AT x= 0.

    This problem does NOT ask if the derivative is continuous at x= 0 so it is not necessary to show that the limit of (1), as x goes to 0, is the same as (2), as I first wrote. (But you might find it interesting to do so.)
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