MAXIMUM MODULUS OF THE DERIVATIVES OF A POLYNOMIAL

For an arbitrary entire function f(z), let M(f;R) = maxjzj=R jf(z)j and m(f; r) = minjzj=r jf(z)j. Let P(z) be a polynomial of degree n, then according to a famous result known as Bernstein's inequality on the derivative of a polynomial, we have M(P0; 1) ≤ nM(P; 1): (1.1) The result is best possible and equality holds for the polynomials having all its zeros at the origin.