I had an assignment that one of my actuarial math teacher gave me and there is a question that need to be proved.
6. Assume that 0<i<1. Show that
a) (1+i)^t < 1+it for 0<t<1
b) (1+i)^t > 1+it for 1<t
HINT: if f(a)=0 and f'(x)>0 for a<x<b then f(b)>0
The problem must be solved with the HINT he gave us.
Thank for your help.