I'm having trouble with the following question regarding limits and rates of change:
A manufacturer's total weekly cost in producing x items can be written as C(x) = F + V(x), where F, a constant, represents fixed costs such as rent and utilities, and V(x) represents variable costs, which depend on production level x. Show that the rate of change of the cost is independent of fixed costs.
I know that obviously it will be, since f remains constant and is not dependent on the x variable. However, I'm not certain how to go about proving it. I thought of maybe setting values for F, V, and X, then using the limit for rate of change to show that it does not change when F does, but that didn't work out. Any help is greatly appreciated Thank you!