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We consider the question if lower estimates in terms of the second order Ditzian-Totik modulus are possible, when we measure the pointwise approximation of continuous function by Bernstein operator. In this case we confirm the conjecture made by Cao, Gonska and Kacsó. To prove this we first establish sharp upper and lower bounds for pointwise approximation of the function g(x) = x ln(x) (1 − x) ln(1 − x), x Î [0, 1] by Bernstein operator.

Mathematics Subject Classification (2010): 41A10, 41A15, 41A25, 41A36.

Keywords: Bernstein operator, lower bounds, Ditzian-Totik moduli of smoothness.