Science:Math Exam Resources/Courses/MATH215/December 2011/Question 03 (b)
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Question 03 (b) |
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For the following ODE (b) Determine the sign of in the regions separated by the equilibrium points. |
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Hint |
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Recall that the derivative can only be zero (and hence change sign) at the fixed points. Therefore these points divide our space into regions where the derivative is either positive or negative. How many regions are there? |
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Solution |
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Please rate my easiness! It's quick and helps everyone guide their studies. From part (a) we have that the equilibrium points are and therefore these points divide our derivative space into four regions where the derivative can be positive or negative, . We have that and we first note that is always positive (unless y = 2) and so the sign of the derivative will be determined by the first term only. For this term we get Therefore Note: We separate the domain of increase for the derivative at the point y=2 because strictly speaking the derivative is not increasing at this point. |