Suppose that is a polynomial. Show that is Lipschitz if and only if the degree of the polynomial is less than 2.
By definition of Lipschitz, then we need to prove that the function p is 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 if p is 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.