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)
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 $\displaystyle a = 0$
use the same formula above, but now, $\displaystyle a$ can be anything but zero. just leave it as $\displaystyle a$ and find the answerif a (can not = 0), find g'(a)
or simply use the power rule to differentiate and plug in $\displaystyle a$
hint: we have a vertical tangent line if the slope is infinite.show that y = x^(2/3) has a vertical tangent line at (0,0)
how does the derivative relate to the slope?