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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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November 18th, 2017, 11:05 PM   #2
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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.
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Last edited by Joppy; November 18th, 2017 at 11:18 PM.
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November 19th, 2017, 12:21 AM   #3
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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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