My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Reply
 
LinkBack Thread Tools Display Modes
July 3rd, 2017, 05:16 PM   #1
Newbie
 
Joined: Jan 2017
From: Canada

Posts: 21
Thanks: 0

Consider the demand equation p = sqrt((200-x)/(2x))

Consider the demand equation p = sqrt((200-x)/(2x))
a) Show that p is decreasing (0,200)
b) Verify that (150, 1/sqrt(6)) is an inflection point of p on (0,200)
c) Let R be the revenue function where 0 < x < 200. Find the maximum revenue
d) Sketch graph of R

I can't get pass part a. From what I have got, the derivative of p has no roots, therefore there is no critical point.
Lalaluye is offline  
 
July 3rd, 2017, 05:55 PM   #2
Global Moderator
 
Joined: May 2007

Posts: 6,379
Thanks: 542

a) The numerator is decreasing, while the denominator is increasing.
mathman is offline  
July 3rd, 2017, 08:52 PM   #3
Senior Member
 
Joined: May 2016
From: USA

Posts: 826
Thanks: 335

Quote:
Originally Posted by Lalaluye View Post
Consider the demand equation p = sqrt((200-x)/(2x))
a) Show that p is decreasing (0,200)
b) Verify that (150, 1/sqrt(6)) is an inflection point of p on (0,200)
c) Let R be the revenue function where 0 < x < 200. Find the maximum revenue
d) Sketch graph of R

I can't get pass part a. From what I have got, the derivative of p has no roots, therefore there is no critical point.
To answer a, there is no need to find critical roots. You can use mathman's clever shortcut or what I expect your teacher wants to see.

Let's go through the calculus way to attack the problem.

What did you get for the derivative of the demand function?

What is its sign over the interval (0, 200)?

What does that mean?

What did you get for the second derivative of the demand function?

Where is that second derivative equal to zero in the designated interval?

How do you derive a revenue function from the demand function?

What are the points where the derivative of the revenue function are zero?

Last edited by JeffM1; July 3rd, 2017 at 08:54 PM.
JeffM1 is online now  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
demand, equation, sqrt200x or 2x



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
Help finding price-demand equation tsl182forever8 Calculus 2 November 16th, 2014 07:24 AM
Help: Demand and supply equation HungerGames1 Economics 0 April 10th, 2012 02:23 AM
Help with a demand equation tsl182forever8 Calculus 3 March 3rd, 2012 07:14 AM
Given the demand equation... tsl182forever8 Calculus 2 February 26th, 2012 10:25 PM
Help with a demand equation tsl182forever8 Algebra 2 December 31st, 1969 04:00 PM





Copyright © 2017 My Math Forum. All rights reserved.