siapa saja tolong jawab pertanyaan ini sama pembahasan

f(x) = -x^3 + 1/2 ax^2 - 1/2 x^2 - 3x + 8
Akan selalu turun jika f'(x) < 0
f'(x) = -3x^2 + ax - x - 3 < 0
=> -3x^2 + (a - 1)x - 3 < 0
=> 3x^2 - (a - 1)x + 3 > 0 ====> definit positif
D < 0 => b^2 - 4ac < 0
=> (-(a - 1))^2 - 4(3)(3) < 0
=> a^2 - 2a + 1 - 36 < 0
=> a^2 - 2a - 35 < 0
=> (a - 7)(a + 5) < 0
=> a = 7 atau a = -5
+++ (-5) --- (7) +++
-5 < a < 7