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A price p (in dollars) and demand x (in items) for a product are related by 2a? + 6xp + 50p : = 23200. If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand The rate of change of demand is items per month.

A price p (in dollars) and demand x (in items) for a product are related by 2a? + 6xp + 50p : = 23200. If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand The rate of change of demand is items per month.

Calculus: Early Transcendentals
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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**Transcription for Educational Website:** **Problem Statement:** You have 3 attempts remaining. A price \( p \) (in dollars) and demand \( x \) (in items) for a product are related by the equation: \[ 2x^2 + 6xp + 5p^2 = 23200. \] If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand. The rate of change of demand is \(\_\_\_\_\) items per month. *(Note: The blank space is intended for the answer to be filled in.)* **Explanation:** This equation relates the price and demand of a product and requires solving for the rate of change of demand with respect to time, given a rate of change of price. This can be solved using implicit differentiation.
Transcribed Image Text:**Transcription for Educational Website:** **Problem Statement:** You have 3 attempts remaining. A price \( p \) (in dollars) and demand \( x \) (in items) for a product are related by the equation: \[ 2x^2 + 6xp + 5p^2 = 23200. \] If the price is increasing at a rate of 2 dollars per month when the price is 20 dollars, find the rate of change of the demand. The rate of change of demand is \(\_\_\_\_\) items per month. *(Note: The blank space is intended for the answer to be filled in.)* **Explanation:** This equation relates the price and demand of a product and requires solving for the rate of change of demand with respect to time, given a rate of change of price. This can be solved using implicit differentiation.
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