Verified answer

f (x) = a x³ + bx² + cx + d

f ''' = 6a = -6 => a = -1

f " = 6a x + 2b = -6x + 2b

f " (-1) = 12 => 6 + 2b = 12 => b = 3

f ' = 3 a x² + 2 b x + c

= -3 x² + 6x + c

=> f ' (-1) = -3 -6 + c = -10 => c = -1

f( -1) = -a + b - c + d = 1 + 3 + 1 + d = 10

=> d = 5

So our cubic polynomial f(x) is

-x³ + 3x² -x + 5