You have a function that you believe to be representative of Marginal Cost. Your task is to determine where this function is increasing or decreasing.
You should let this description roll around a bit in your brain. This is an ideal question for a derivative. Derivatives provide this kind of information.
Expressed as a function of x, C'(x) = -0.006x^2 - 0.12x + 120
We need the derivative of C'(x) - this is the second derivative of C(x). C"(x) = -0.012x - 0.12
You should be able to figure out where C"(x) is positive, negative, or zero.
One more thing: As C(x) may describe a real quantity, you will need to consider it's Domain. I'm guessing x >= 0. Is there an upper limit?