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.
