Problem:

Suppose that is a polynomial. Show that is Lipschitz if and only if the degree of the polynomial is less than 2.

Attempt:

By definition of Lipschitz, then we need to prove that the functionpis Lipschitz for degree less than 2 or equivalently then

for and for all

Here I'm not sure how to approach this. Since p is a polynomial, then it must be continuous. I was thinking of showing that ifpis a polynomial of less than 2, then its derivative is a constant. Thus, its derivative is bounded and therefore a Lipschitz function.

Thank you for your time.