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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- Oct 24th 2008, 02:08 PMcm3pyrolimits / 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) - Oct 24th 2008, 02:14 PMJhevon
the derivative of a function $\displaystyle g(x)$ at the point $\displaystyle x = a$ exists if and only if the limit

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

exists

just show this limit does not exists if $\displaystyle a = 0$

Quote:

if a (can not = 0), find g'(a)

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

Quote:

show that y = x^(2/3) has a vertical tangent line at (0,0)

how does the derivative relate to the slope?