Prove that the function $f(x) = x^n$, $n \in \mathbb{N}$ and $n>2$:
a. is Lipschitz continuous in every bounded interval.
b. is not Lipschitz continuous in every non-bounded interval.
My attempt: I've tried to prove it's Lipschitz and I ended up finding that $C=|x_1^{n-1} - x_2^{n-1}| >0$. I don't know what else to do.