1. ## Marginal Profit

A certain item sells for $30. If the cost of producing this item is given by C=.05x^3+100, find the marginal profit when x=10. So i know P(rofit)=R-C and marginal Profit =dP/dx but im not sure how you find R and when you plug in 10 for x and$30

2. Revenue will be price times number sold, so...

... where straight lines differentiate downwards with respect to x.

Spoiler:

Obviously plug in for x now, in the derivative expression.

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3. I don't know how you got the 30x-1/2x^3-100

4. Originally Posted by rawkstar
I don't know how you got the 30x-1/2x^3-100
Some of it's R and some of it's C...

5. Originally Posted by tom@ballooncalculus
Some of it's R and some of it's C...

man Tom...nice style with the spoliers and all that. what prime pedagogy.

6. howd u get R?

7. Originally Posted by tom@ballooncalculus
Revenue will be price times number sold, so...
.....

8. thanks but shouldnt P=30x-.05x^3-100 since C=.05x^3+100?

9. Originally Posted by rawkstar
thanks but shouldnt P=30x-.05x^3-100 since C=.05x^3+100?
Gosh, yeah - never saw that zero!

Will correct the pics

10. ## Re: Marginal Profit

I do not understand where the 1/20 came from. How did you build that equation? And when you plug in x (which is 10), I get -120 and my answer sheet says 15.

11. ## Re: Marginal Profit

Originally Posted by mathidiot123
I do not understand where the 1/20 came from. How did you build that equation? And when you plug in x (which is 10), I get -120 and my answer sheet says 15.
note that $\displaystyle 0.05 = \frac{1}{20}$

$\displaystyle \frac{dP}{dx} = 30 - 0.15x^2$

evaluated at $x = 10$ ...

$\displaystyle \frac{dP}{dx}_{x=10} = 30 - 0.15(10^2) = 30 - 15 = 15$