Marginal cost and marginal revenue

[newts]

Homework Statement

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

Homework Equations

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

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.

 

[Ray Vickson]

Homework Statement

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

Homework Equations

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

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.

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

RGV

 

[newts]

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

RGV

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?

 

[Mark44]

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

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).

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