=+21. Suppose the function f(x) has continuous derivative f (x). For > 0 show that Bernsteins

=+21. Suppose the function f(x) has continuous derivative f

(x). For δ > 0 show that Bernstein’s polynomial satisfies the bound E



f

Sn n

 − f(x)

≤ δ||f

||∞ + ||f||∞

2nδ2 .

Conclude from this estimate that

E



f

Sn n

 − f

∞ = O(n− 1 3 ).

3.6 Problems 73