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The marginal cost and marginal revenue for $x$ items in dollars is given by the equations $C^{\prime}(x)=70,$ and $R^{\prime}(x)=-0.1 x+900 .$ If the overhead cost is $\$ 800,$ determine the profit function.

$$P(x)=-0.05 x^{2}+830 x-800$$

Calculus 1 / AB

Chapter 5

Integration and its Applications

Section 2

Applications of Antidifferentiation

Integrals

Oregon State University

Harvey Mudd College

University of Nottingham

Idaho State University

Lectures

05:53

In mathematics, an indefinite integral is an integral whose integrand is not known in terms of elementary functions. An indefinite integral is usually encountered when integrating functions that are not elementary functions themselves.

40:35

In mathematics, integration is one of the two main operations of calculus, with its inverse operation, differentiation, being the other. Given a function of a real variable (often called "the integrand"), an antiderivative is a function whose derivative is the given function. The area under a real-valued function of a real variable is the integral of the function, provided it is defined on a closed interval around a given point. It is a basic result of calculus that an antiderivative always exists, and is equal to the original function evaluated at the upper limit of integration.

02:10

Let C(x) be the cost funct…

03:10

Suppose the cost function …

02:48

04:35

Cost, revenue, and profit …

01:18

Let $R(x)$ be the revenue …

01:13

For each cost function, fi…

02:17

Cost Find the cost functio…

02:14

Find the marginal cost for…

02:20

Find the marginal cost, ma…

01:30

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