## NEED HELP to proof that a function f(t) is bigger than a function g(t)

Hello everyone,

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

f(t)=
(1+i)^t
g(t)=
1+it

a) f(t) < g(t) for 0<t<1

b)
f(t) > g(t)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.