Prove $(1+z)^a \geq 1+az$, for $z>-1, a>1$, using the mean value theorem
Hint says try using: $f(z)=(1+z)^a$
I've tried messing around with this, but I can't seem to get 1 + az on the RHS. I'm struggling a little. Would appreciate help on this. Must be some simple trick that I'm missing.