so as the title states I have the following problem where I have to show:
$(1+x)^r > 1+rx$
$r>1$ and if $x>0$ or $-1\le x<0$
So im having alot of trouble with the intution for solving inequalties where one thing implies the other, I don't think you have to apply MVT on this problem since the formula did't.
But could I problem the inequality by doing the following:
$f(x)= (1+x)^r -(1+rx)$
Could I say that for $f'(x)>0$ to be larger than 0, i.e increasing.
$(1+x)^r>(1+rx)$ in order for $f'(x)$ to increase for $x>0$