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Exercise 3.2.10 Suppose we try to evaluate the stability of the X = 0 equilibrium point of the vector field X' = 2X2 X a) Perform a linear stability analysis at the point X = 0. What is the character ofthis equilibrium point according to this analysis? b) Suppose we did a test point analysis for confirmation and chose two test points, X = 1 and X = +1. When we calculate the change vectors X' at these two points, we see that the change vector at X = 1 is positive, X'|X=_1 = 2(1)2 (1) = 3 and the change vector at X = +1 is also positive, = 2(+1)2 (+1) = 1 Explain why this test point method conflicts with the linear stability analysis. What have we done wrong? (Hint: Plot the X " function.) Xle=+1