it might be a silly question but I tried everything and could not find the possible error.
I got
$ f(x) = e^x $
and I have to find all possible boundary points of $f(x)$ with tangent(s), which go through the point
$ P (1/1) $
Well, I'll just post what I did.
\begin{align} \frac{1-e^x}{1-x} &= f'(x) \\ \frac{1-e^x}{1-x} &= e^x \\ 1-e^x &= e^x - e^x\cdot x \\ 1+e^x\cdot x &= 2\cdot e^x \end{align}
...
edit: Thanks for the advice. Ok I'm stuck and I think on the wrong way.
Well I thought, the slope of that unknown tangent with $P(1/1)$ has to be the same as the derivative of the point I am looking for. $P$ obviously is not part of $f(x)$.
Maybe there's another way. I just need a hint. Thank you.