My Math Forum Curve Sketching

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November 18th, 2017, 10:39 PM   #1
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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.
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 Q4pt1.jpg (19.7 KB, 13 views) Q4pt2.jpg (20.3 KB, 8 views)

 November 18th, 2017, 11:05 PM #2 Senior Member   Joined: Feb 2016 From: Australia Posts: 1,838 Thanks: 653 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 18th, 2017 at 11:18 PM.
 November 19th, 2017, 12:21 AM #3 Senior Member   Joined: Jun 2015 From: England Posts: 915 Thanks: 271 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

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