Function f (x) = (1 + x-x22 + x33-x44 + -The number of zeros of cos2x on interval [- 3, 3] is () A. 3B. 4C. 5D. 6

Function f (x) = (1 + x-x22 + x33-x44 + -The number of zeros of cos2x on interval [- 3, 3] is () A. 3B. 4C. 5D. 6

Let g (x) = 1 + x-x22 + x33-x44 + -Then G ′ (x) = 1-x + x2-x3 + +X2012 = 1 + x20131 + X, in the interval [- 3, 3], 1 + x20131 + X ＞ 0, so the function g (x) is an increasing function in [- 3, 3]. Because the exponent of X on the right side of G (- 3) formula is negative before even degree term and positive before odd number term, the result must be negative, that is, G (- 3) ＜ 0, and G (3) = 1 + 3 + (- X22 + x33) + (- x44 + x55) + +(- x2012012 + x20132013) > 0, so the function g (x) has and only has one zero point on [- 3,3]. And y = cos2x has four zero points on the interval [- 3,3] and does not repeat the zero points mentioned above. The function f (x) = (1 + x-x22 + x33-x44 + -The number of zeros of cos2x in the interval [- 3, 3] is 1 + 4 = 5