Let the curve y = ax ^ 3 + BX ^ 2 + CX + 2 have a minimum value of 0 at x = 1, and the point (0,2) is the inflection point of the curve,

Let the curve y = ax ^ 3 + BX ^ 2 + CX + 2 have a minimum value of 0 at x = 1, and the point (0,2) is the inflection point of the curve,

Take point (1,0) into a + B + C + 2 = 0, because the extreme value is obtained at point (1,0), the value of the first derivative y ′ = 3ax ^ 2 + 2bx + C at this point is zero, so there is 3A + 2B + C = 0, and point (0,2) is the inflection point of the curve, so at this point, the value of the second derivative y ″ = 6AX + 2b is zero, then 2B = 0, the solution of the equations is: a = 1, B = 0, C = - 3

If we know that the real numbers a, B, C and D are in equal proportion sequence, and the coordinates of the maximum point of the curve y = 3x-x3 are (B, c), then ad is equal to ()
A. 2B. 1C. -1D. -2

∵ y ′ = 3-3x2 = 0, then x = ± 1, ∵ y ′ < 0, we can get x ＜ - 1 or X ＞ 1, y ′ > 0, we can get - 1 ＜ x ＜ 1, ∵ function monotonically decreases on (- ∞, - 1), (1, + ∞), monotonically increases on (- 1,1), ∵ x = 1 is the maximum point, at this time, the maximum is 3-1 = 2