If a cubic function has a maximum value of 4 when x = 1 and a minimum value of 0 when x = 3, and the function image crosses the origin, then the function is () A. y=x3+6x2+9xB. y=x3-6x2-9xC. y=x3-6x2+9xD. y=x3+6x2-9x

If a cubic function has a maximum value of 4 when x = 1 and a minimum value of 0 when x = 3, and the function image crosses the origin, then the function is () A. y=x3+6x2+9xB. y=x3-6x2-9xC. y=x3-6x2+9xD. y=x3+6x2-9x

Let the cubic function be y = AX3 + bx2 + CX + D, because it passes through the origin, so the constant term is d = 0 ∪ y = AX3 + bx2 + CX ∪ y '= 3ax2 + 2bx + C. because the function has a maximum of 4 when x = 1 and a minimum of 0 when x = 3, 3ax2 + 2bx + C = 0 has two real roots 1 and 3 ∪ 1 + 3 = − 2b3a1 × 3 = c3aa + B + C = 4 ∪ a = 1, B = -