# limits / derivates question

• Oct 24th 2008, 02:08 PM
cm3pyro
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)
• Oct 24th 2008, 02:14 PM
Jhevon
Quote:

Originally Posted by cm3pyro
if g(x) = x^(2/3) show that g'(0) does not exist.

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)
use the same formula above, but now, $\displaystyle a$ can be anything but zero. just leave it as $\displaystyle a$ and find the answer

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)
hint: we have a vertical tangent line if the slope is infinite.

how does the derivative relate to the slope?