# How to derive a marginal cost curve [closed]

Provide a mathematical proof for the general result that, given a linear average curve, the corresponding marginal curve must have the same vertical intercept but will be twice as steep as the average curve

## closed as off-topic by Giskard, BKay, optimal control, cc7768, LumiOct 8 '15 at 21:43

This question appears to be off-topic. The users who voted to close gave this specific reason:

• "This question does not appear to be about economics, within the scope defined in the help center." – Giskard, BKay, optimal control, cc7768, Lumi
If this question can be reworded to fit the rules in the help center, please edit the question.

• Hi, welcome to Economics SE. We tend to ask users to give some evidence that they have tried to do things that look like homework questions before just posting a question. The guidelines are readily available to you in the help section. – Kitsune Cavalry Oct 8 '15 at 0:41

That comment said, I can provide an answer here.

Take an average cost function:

$$f(x) = mx + b$$ where x is output, b is the intercept, and m is the gradient.

So total cost is:

$$C(x) = x(mx + b) = mx^2 + bx$$

And that makes marginal cost the derivative of this function:

$$C'(x) = 2mx + b$$

Best of luck with your homework.

• If you disagree with your own comment you don't have to say it, if you agree with the comment why do you answer? – Giskard Oct 8 '15 at 6:24
• "We tend to ask users"... Sometimes we can give new people a break I think. – Kitsune Cavalry Oct 8 '15 at 14:33