- #1
mk9898
- 109
- 9
Homework Statement
Let f be ##f:[0,\infty]\rightarrow \mathbb R
\\
f(x):=
\begin{cases}
e^{-x}sin(x), \ if \ \ x\in[2k\pi,(2k+1)\pi] for \ a \ k \in \mathbb N_0 \\
0 \ \ otherwise\\
\end{cases}##
Exercise: Determine all inner points of the domain where f is also differentiable and determine f' at these points.
The Attempt at a Solution
Idea:
Since we only need to look at inner differentiable points, we can look at points all points where f'(x) = 0. These are the only differentiable points because this is where the second case of f is a constant i.e. f'(x') = 0 for all x' in the second case. So we need to look for the points in the first case, where f'(x'')=0 and x'' is in these closed intervals for the first case. These are the differentiable inner points.
If I am on the right track, then I am wondering how I could find all of the points where that is valid for the first case of f.