1. The problem statement, all variables and given/known data Prove that the equation [tex]e^x = 1+x[/tex] admits the unique solution [tex]x_0 = 0[/tex]. 2. The attempt at a solution I think there should be a very simple proof based on monotonicity or the absence of inflection points, etc. But I have no idea how to do it, and what theorems are to be used. All I can say from the equation, is that if there are solutions, they certainly satisfy [tex] x>-1[/tex] I'm actually a little ashamed that I can't do this, most likely, trivial problem, maybe somebody can show me the right path?