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Math Help - limits / derivates question

  1. #1
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    limits / derivates question

    if g(x) = x^(2/3) show that g'(0) does not exist.
    if a (can not = 0), find g'(a)
    show that y = x^(2/3) has a vertical tangent line at (0,0)
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by cm3pyro View Post
    if g(x) = x^(2/3) show that g'(0) does not exist.
    the derivative of a function g(x) at the point x = a exists if and only if the limit

    \lim_{h \to 0} \frac {g(a + h) - g(a)}h

    exists

    just show this limit does not exists if a = 0

    if a (can not = 0), find g'(a)
    use the same formula above, but now, a can be anything but zero. just leave it as a and find the answer

    or simply use the power rule to differentiate and plug in a

    show that y = x^(2/3) has a vertical tangent line at (0,0)
    hint: we have a vertical tangent line if the slope is infinite.

    how does the derivative relate to the slope?
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