are the solutions of stable $x' = x(1-x)$?

Question

I had difficulties finding the answer to the following question:

Determine whether the solutions $x(t) = 0$ and $x(t) = 1$ of the single scalar equation $x' = x(1-x)$ are stable or unstable.

I tried to do this with the definition for stability but I wasn't able to find eigenvalues here

Answer 1

'Nough said? $$-\!\!-\!\!-\!\!\!\!-\!\!-\!\!-\!\!\longleftarrow\!\longleftarrow\!\longleftarrow\!\!-\!\!-\!\!-\!\!\stackrel{0}{\otimes}\!\!-\!\!-\!\!-\!\!\longrightarrow\!\longrightarrow\!\longrightarrow\!\!-\!\!-\!\!-\!\!-\!\!-\!\!-\!\!\stackrel{1}{\otimes}\!\!-\!\!-\!\!-\!\!-\!\!-\!\!-\!\!\longleftarrow\!\longleftarrow\!\longleftarrow\!\!-\!\!-\!\!-$$