We have f ' (x) = 6x2 + 6x - 432, so f '' (x) = 12x+6 correct: your answer is correct., which equals 0 when

The derivative of the first derivative given to be, f' (x) = 6x² + 6x - 432 is given to be,

f'' (x) = 12x + 6

As asked in the given, the value of the second derivative becomes zero when the value of x is,

f" (x) = 0 = 12x + 6

12x + 6 = 0

Subtract 6 from both sides of the equation such that,

12x = - 6

Divide both sides of the equation by 12 giving us an answer of

x = - 1/2.

Hence, x = - 1/2.