Let f (x) = AX2 + BX + C (a, B, C ∈ R). If x = - 1 is an extreme point of the function y = f (x) ex, then the following image cannot be () A. B. C. D.

Let f (x) = AX2 + BX + C (a, B, C ∈ R). If x = - 1 is an extreme point of the function y = f (x) ex, then the following image cannot be () A. B. C. D.

From y = f (x) ex = ex (AX2 + BX + C) {y ′ = f ′ (x) ex + ExF (x) = ex [AX2 + (B + 2a) x + B + C], from x = - 1 as an extreme point of function f (x) ex, - 1 is a root of equation AX2 + (B + 2a) x + B + C = 0, so there is a - (B + 2a) + B + C = 0 {C = a