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Math Help - Differentiable piecewise function

  1. #1
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    Differentiable piecewise function

    My task is as follows:
    Let  f(x) = x^2 \text{for } x \geq 0 \wedge f(x) = 0 \text{for } x < 0.
    B. Show that f is differentiable at  x = 0.
    C. Calculate  f' \text{on } \mathbb{R}.

    Any help will be greatly appreciated.

    -the Doctor
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by thedoctor818 View Post
    My task is as follows:
    Let  f(x) = x^2 \text{for } x \geq 0 \wedge f(x) = 0 \text{for } x < 0.
    B. Show that f is differentiable at  x = 0.
    C. Calculate  f' \text{on } \mathbb{R}.

    Any help will be greatly appreciated.

    -the Doctor
    I don't understand. It's clearly differentiable on \mathbb{R}-\{0\} and \lim_{x\to0^-}\frac{f(x)-f(0)}{x-0}=\lim_{x\to 0^-}0=0=\lim_{x\to0^+}2x=\lim_{x\to0^+}\frac{f(x)-f(0)}{x-0}
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  3. #3
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    Since the  lim_{x\to0-}=lim_{x\to0+} then does that mean that  f(x) \; \text{is differentiable at } x=0 ?
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