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The marginal cost for $x$ items in dollars is given by $C^{\prime}(x)=2 x+50 .$ If the overhead cost is $\$ 5,000,$ determine the cost function.

$$x^{2}+50 x+5000$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 2

Applications of Antidifferentiation

Integrals

Baylor University

University of Nottingham

Idaho State University

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Okay, so we're giving a marginal cost function as well as two units. Costs $5.50. So that is our cost function. Evaluated at 20 to 5. What? 50. Okay. And we have to find our cost function. So notice here that we have the derivative of our cost function, so we can just take the integral of that. Your evidence. And that should give us our cost function. Plus some constant k. Okay, so let's solve for that. So starting with the integral of X plus one over X squared, we get the falling. Let's use our some world just work out up into two intervals. I will also be right one over X squared as a negative exponents. Okay, I know using a powerful begets extra car to over to what exit? Power of negative one over negative one. So that's equal to negative one over X. That's okay. Okay. And this is our cost function with an arbitrary constants, kid. Another tier of that we have see of two is equal to 5.5. So let's put that into find RK So we have five points. 50 is equal to I want you to. So that's two squared off to one. It's 1/2 plus K. So that gives me four of the two, which is two minus one have plus K and 5.5. So too, is for over two. That's equal to three over to K and 5.5. So 5.5 minus 3/2 gives me four. So we have our constants is equal to four. Okay, so let's just replace R K value with that for so this is equal to our cost function.

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