What is the total-profit function? dPA firm has the marginal-profit function20,000 - 5000x2, where P(x) is the profit earned at x dollars per unit. Find the total-profit function given that P= $2500 at x = $4.%3DxpHow can the total-profit function be found?OA. Substitute the given value of x into the marginal-profit function and evaluate.OB. Substitute the given value of P into the marginal-profit function and solve for x.OC. Find the derivative of the marginal-profit function and use the given values of x and P to find C.D. Find the antiderivative of the marginal-profit function and use the given values of x and P to find C.Find the total-profit function.P(x) =O

Given: dPdx=20,000−5,000x(x2−8x+17)2

Answered: 20,000 - 5000x dP A firm has the…

20,000 - 5000x dP A firm has the marginal-profit function where P(x) is the profit earned at x dollars per unit. Find the total-profit function given that P= $2500 at x = $4. %3D xp (x? - 8x + 17) 2

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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Question

What is the total-profit function?

dP
A firm has the marginal-profit function
20,000 - 5000x
2, where P(x) is the profit earned at x dollars per unit. Find the total-profit function given that P= $2500 at x = $4.
%3D
xp
How can the total-profit function be found?
OA. Substitute the given value of x into the marginal-profit function and evaluate.
OB. Substitute the given value of P into the marginal-profit function and solve for x.
OC. Find the derivative of the marginal-profit function and use the given values of x and P to find C.
D. Find the antiderivative of the marginal-profit function and use the given values of x and P to find C.
Find the total-profit function.
P(x) =O

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