It is known that the value of X which makes the derivative of the function y = X3 + ax2-43a 0 also makes the value of y 0, then the value of constant a is () A. 0b. ± 3C. 0 or ± 3D

It is known that the value of X which makes the derivative of the function y = X3 + ax2-43a 0 also makes the value of y 0, then the value of constant a is () A. 0b. ± 3C. 0 or ± 3D

The derivative of the function is y ′ = 3x2 + 2aX = 0, the solution is x = 0 or x = - 23a, when x = 0, the function value is y = 0, that is - 43A = 0, at this time a = 0, when x = - 23a, the function value is y = 0, that is (− 23a) 3 + a (− 23a) 2-43a = 0, the solution is a3-9a = 0, that is a (a2-9), the solution is a = 0 or a = ± 3, so choose: C