# Marginal cost and marginal revenue

1. Oct 24, 2012

### newts

1. The problem statement, all variables and given/known data

For a certain product, cost C and revenue R are implicitly given as follows, where x is the number of units sold (in hundreds)
a) Find and interpret the marginal cost dC/dx at x=5
b) Find and interpret the marginal revenue dR/dx at x=5

2. Relevant equations

C2 = x2+100√x +50
900(x-5)2 + 25R2 = 22500

3. The attempt at a solution

So I think I'm making this out to be a lot harder than it actually is. My first instinct would be to apply derivatives and chain rule.

2. Oct 24, 2012

### Ray Vickson

Why don't you just go ahead and do that, to see what you get?

RGV

3. Oct 24, 2012

### newts

Okay, so then because C defines x implicitly, we'll be looking for implicit derivatives, right? So with that, I get my marginal cost to be

c'= (2x + 50/√x)/2c

And then from there, I would plug in my x=5

But I'm thinking that equation might be wrong? Because what would I do with the 2c in the denominator?

4. Oct 25, 2012

### Staff: Mentor

What you have looks OK, except that you should have parentheses around 2C in the denominator.

Use the cost equation to find C when x = 5, and then find C'(x).