Answer: C) -1/2
=============================================
Step-by-step explanation:
We'll apply the derivative to get
g(x) = 4x^3 + 3x^2
g ' (x) = 3*4x^2 + 2*3x
g ' (x) = 12x^2 + 6x
Set that equal to 0 and solve for x. We do this to find where the horizontal tangents are located.
g ' (x) = 0
12x^2 + 6x = 0
6x(2x + 1) = 0
6x = 0 or 2x+1 = 0
x = 0 or x = -1/2
Adding those two said solutions yields us the final answer choice C