The question reads very simply, show that ex [tex]\geq[/tex]1+x [tex]\forall[/tex] x > 0
None to speak of. I am not allowed to use calculus, and this is why I am having problems.
The Attempt at a Solution
I tried to break it up into cases:
When x=0, ex=e0=1 1+x=1+0=1
Then I decided to take the natural log of both sides and try my hand at the other three cases (which I think should be 0<x<1, x=1, and x>1):
ln2<x is easy, but I cannot even imagine how I would be able to solve the other cases.