Suppose n > 1 is a positive integer. Prove $\displaystyle x^n > x $for all x > 1.

(hint: suppose we know f and g are differentiable on the interval (-c,c) and f(0) = g(0), if f'(x) > g'(x) for all $\displaystyle x \in(0,c)$, then f(x) > g(x) for all $\displaystyle x \in (0,c)$.