A student studies the function f (x) = xsinx and draws the following four conclusions: 1) the function f (x) increases monotonically on [− π 2, π 2]; 2) there is a constant M > 0, so that | f (x) | ≤ m | x | holds for all real numbers x; 3) the function f (x) has no minimum value at (0, π), but must have a maximum value; 4) the point (π, 0) is a symmetry center of the function y = f (x) image （　　） A. ③B. ②③C. ②④D. ①②④

A student studies the function f (x) = xsinx and draws the following four conclusions: 1) the function f (x) increases monotonically on [− π 2, π 2]; 2) there is a constant M > 0, so that | f (x) | ≤ m | x | holds for all real numbers x; 3) the function f (x) has no minimum value at (0, π), but must have a maximum value; 4) the point (π, 0) is a symmetry center of the function y = f (x) image （　　） A. ③B. ②③C. ②④D. ①②④

① F (- x) = - xsin (- x) = f (x), it is easy to know that f (x) is an even function, so f (x) = xsinx can not increase monotonically on [− π 2, π 2]; ② taking M = 1 shows that the conclusion is correct; ③ from ② we know that | f (x) | ≤| x |, so there must be a maximum value in (0, π), because f (x) > 0, and there is no relation with 0