<p>That comment said, I can provide an answer here.</p>

<p>Take an average cost function:</p>

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

<p>So total cost is:</p>

<p>$$C(x) = x(mx + b) = mx^2 + bx$$</p>

<p>And that makes marginal cost the derivative of this function:</p>

<p>$$C'(x) = 2mx + b$$</p>

<p>Best of luck with your homework.</p>

CC BY-SA 3.0
2015-10-08T06:24:53.427Z
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
CC BY-SA 3.0
2015-10-08T14:33:37.907Z
"We _tend_ to ask users"... Sometimes we can give new people a break I think.
Kitsune Cavalry
CC BY-SA 3.0
2015-10-08T00:44:49.610Z
2015-10-08T00:44:49.610Z
Kitsune Cavalry
<p>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 </p>

CC BY-SA 3.0
2015-10-08T00:41:11.983Z
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
<cost>
How to derive a marginal cost curve
michael
# How to derive a marginal cost curve

(Asked by: username_0 on 2015-10-08)

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

**Tags:** cost

> **Comments:**
> **username_1**: 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.  

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## 1 answers

### Answer by username_1 on 2015-10-08. Score: 2

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.

> **Comments:**
> **username_2**: If you disagree with your own comment you don't have to say it, if you agree with the comment why do you answer?  
> **username_1**: "We _tend_ to ask users"... Sometimes we can give new people a break I think.  

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