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Math Help - Proving an equation is non-differentiable?

  1. #1
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    Proving an equation is non-differentiable?

    Hi,

    How would I go about formally proving that a continuous equation e.g. y=|x| is non-differentiable at a point such as x=0?

    I know what it looks like graphically with a sharp edge but how would the proof look like algebraically?
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  2. #2
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    Show that \lim _{h \to 0^ +  } \frac{{\left| {0 + h} \right| - \left| 0 \right|}}{h} \ne \lim _{h \to 0^ -  } \frac{{\left| {0 + h} \right| - \left| 0 \right|}}{h}
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  3. #3
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    Quote Originally Posted by Plato View Post
    Show that \lim _{h \to 0^ +  } \frac{{\left| {0 + h} \right| - \left| 0 \right|}}{h} \ne \lim _{h \to 0^ -  } \frac{{\left| {0 + h} \right| - \left| 0 \right|}}{h}
    Wouldn't they both converge to 0 on both sides of the curve?
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  4. #4
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    Quote Originally Posted by Kataangel View Post
    Wouldn't they both converge to 0 on both sides of the curve?
    Neither of those limits is zero.
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