Explaining 3 True/False Questions About Calculus

[IntegrateMe]

After a long series of true/false questions from my calculus book, I'm left with three I don't really understand. Anyone care to explain them to me?

A) If f and g are differentiable increasing functions and g(x) is never equal to 0, then the function h(x) = f(x)/g(x) is also a differentiable increasing function.

B) If a function is period with period c, then so is its derivative.

C) If C(q) represents the cost of producing a quantity q of good, then C'(0) represents the fixed costs.

 

[Fredrik]

When you post a question about a textbook-style problem, you're expected to show some of your own work. In this case, you should have told us what you have tried so far.

A) I don't see a way to give you a hint without telling you too much. What have you tried so far?
B) You're supposed to find out if the following is true: If f(x+c)=f(x) for all x, then f'(x+c)=f'(x) for all x. What do you get if you use the definition of the derivative to rewrite f'(x+c)?
C) How do you define "fixed costs"?

 

[IntegrateMe]

In part C, "fixed costs" is what most tripped me up, I have no idea what that means...

 

[Fredrik]

Hm, C is a bit ambiguous. I would interpret it like this: q is the amount you manufacture in some fixed time, say a month. C(q) is what it costs to do that. The "fixed costs" is the amount of money you have to spend during that time, just to be able to manufacture anything at all. Something like the rent for one month.

 

[D H]

With regard to C, what does your text define as "fixed cost"? Do they have a graph of C(q)?