November 18th, 2017, 11:39 PM  #1 
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.

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. Last edited by Joppy; November 19th, 2017 at 12:18 AM. 
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? 

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