Let ii denote the set of all monic polynomials of degree n Theorem The polynomials of the form Tn(a), when n 2 1, have the property that =max,|n(x)≤max,|Pn(x), for all Pn(x)∈Il r∈[-1,1 x∈[-1,1 Moreover, equality can occur only if P=T, Proof. Suppose Pn(a)E Il and maX maX r∈[-1,1 ∈[-1,1 Let Q=Tn-Pn Since Tn(a) and P(a)are both monic polynomials of degree m, Q(a) is a polynomial of degree at most(n-1) oreover at the extreme points k Tk of Tn(a) 2)=(x)-P()=(-1