- #1
Ryker
- 1,086
- 2
Homework Statement
[tex]\begin{displaymath}
f(x) = \left\{
\begin{array}{lr}
e^{- \frac{1}{x^{2}}} & : x \neq 0 \\
0 & : x = 0
\end{array}
\right.
\end{displaymath} [/tex]
What is the derivative of f(x) at x = 0, that is, what is f'(0)?
The Attempt at a Solution
I am a bit lost on how to show that f'(0) = 0. I've tried doing it from the definition of the derivative, but then I get
[tex]\displaystyle\lim_{x\to 0}\frac{e^{- \frac{1}{x^{2}}}}{x}[/tex]
and I don't know how to proceed. L'Hôpital's rule doesn't seem to help here, either. Any suggestions?