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A company is increasing the production of a product at the rate of 20 units per week. The demand and cost functions for the product are given by p = 50 − 0.02x and C = 4000 + 40x − 0.04x2, where x is the number of units produced per week. Find the rate of change of the profit with respect to time (in dollars per week) when the weekly sales are x = 700 units.

A company is increasing the production of a product at the rate of 20 units per week. The demand and cost functions for the product are given by p = 50 − 0.02x and C = 4000 + 40x − 0.04x2, where x is the number of units produced per week. Find the rate of change of the profit with respect to time (in dollars per week) when the weekly sales are x = 700 units.

Algebra and Trigonometry (MindTap Course List)
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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A company is increasing the production of a product at the rate of 20 units per week. The demand and cost functions for the product are given by 

p = 50 − 0.02x

 and 

C = 4000 + 40x − 0.04x2,

 where x is the number of units produced per week. Find the rate of change of the profit with respect to time (in dollars per week) when the weekly sales are 

x = 700 units.
A company is increasing the production of a product at the rate of 20 units per week. The demand and cost functions for the product are given by p = 50 - 0.02x and C = 4000 + 40x – 0.04x2, where x is the number of units produced per week. Find the rate of change of the profit with respect to time (in dollars per week) when the weekly sales are x = 700 units. $ per week
Transcribed Image Text:A company is increasing the production of a product at the rate of 20 units per week. The demand and cost functions for the product are given by p = 50 - 0.02x and C = 4000 + 40x – 0.04x2, where x is the number of units produced per week. Find the rate of change of the profit with respect to time (in dollars per week) when the weekly sales are x = 700 units. $ per week
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