My Math Forum  

Go Back   My Math Forum > College Math Forum > Calculus

Calculus Calculus Math Forum


Thanks Tree2Thanks
  • 1 Post By Joppy
  • 1 Post By studiot
Reply
 
LinkBack Thread Tools Display Modes
November 18th, 2017, 11:39 PM   #1
yli
Newbie
 
Joined: Oct 2017
From: ...

Posts: 5
Thanks: 0

Curve Sketching

Hi, I was wondering if I could get some help of how I should begin the sketching of the graphs. Also any help with how I should approach the other parts of the question is greatly appreciated.
Attached Images
File Type: jpg Q4pt1.jpg (19.7 KB, 13 views)
File Type: jpg Q4pt2.jpg (20.3 KB, 8 views)
yli is offline  
 
November 19th, 2017, 12:05 AM   #2
Senior Member
 
Joined: Feb 2016
From: Australia

Posts: 1,460
Thanks: 489

Math Focus: Yet to find out.
Stick dP/dt on the vertical axis (this is your 'output') and stick P on the horizontal axis (your 'input'), sketch as you usually would.

Equilibrium points necessarily occur when P' = 0. It is stable if the derivatives to the left and right of P are increasing and decreasing respectively. Updating your sketch from a) in part b) may help.

EDIT: Sorry, not to the 'left and right of P', but to the left and right of a zero of P'. e.g. In a), P = K is a stable equilibrium point.
Thanks from yli

Last edited by Joppy; November 19th, 2017 at 12:18 AM.
Joppy is offline  
November 19th, 2017, 01:21 AM   #3
Senior Member
 
Joined: Jun 2015
From: England

Posts: 704
Thanks: 202

What happens to your plot when P = K ?

Are there any other points where this happens?

Are there any discontinuities in this plot?
Thanks from yli
studiot is offline  
Reply

  My Math Forum > College Math Forum > Calculus

Tags
curve, sketching



Thread Tools
Display Modes


Similar Threads
Thread Thread Starter Forum Replies Last Post
curve sketching Lima Calculus 1 April 1st, 2013 09:08 PM
curve sketching.... pomazebog Calculus 3 March 25th, 2012 06:50 PM
curve sketching help!!!!!! chris li Calculus 5 November 21st, 2011 08:38 AM
Curve Sketching hunnybee Calculus 7 March 22nd, 2011 11:55 PM
Curve Sketching chrisf Calculus 2 November 21st, 2008 01:47 PM





Copyright © 2017 My Math Forum. All rights reserved.