So the full question goes as following:
If $x>0$ or $-1\le x<0$, show that $(1+x)^r < (1+rx)$
I'm having a real hard time getting the idea of the usefullness of MVT. It seems every approach I take is faulty.
I don't know how to think. If I take $f'(c)$ for $0<c<x$ I get $(1+c)r -1 / c$ which I can conclude is larger than $0$, which leads me nowhere.
Help is very appriciated!