Some calculus problems in the assignment of Calculus 1 course

1) a) show that e^x >= 1 + x for x>=0

b) deduce that e^x >= 1 + x + 1/2 x^2 for x >= 0

c) use mathematical induction to prove that for x >= 0 and any positive integer n,

e^x >= 1 + x + x^2 / 2! + ... + x^n / n!

2) Show that cubic function ( a third degree polynomial ) always has exactly 1 point of inflection. If it's graph has 3 x-intercepts x1, x2, x3, show that the x coordinate of the inflection point is (x1+x2+x3) / 3

i've been stuck with these problems for a while (luckily, other 100 problems are easier (Rofl)) plz help me, deadline is coming ~.~ thks a lot!!