Dini bounds for differentiated Bernstein polynomials

The well-known fact that () of the sequence of Bernstein polynomials of a bounded function is bounded above (below) by the average value of the two upper (lower) limits of the function is supplemented with the following derived version: () of the sequence of derived Bernstein polynomials is bounded above (below) by the average value of the two upper (lower) Dini derivatives.