Let f (y) be a continuous function.
(a) Suppose that f (−10) > 0 and f (10) < 0. Show that there is an equilibrium point for dy/dt = f (y) between y = −10 and y = 10.
(b) Suppose that f (−10) > 0, that f (10) < 0, and that there are finitely many equilibrium points between y = −10 and y = 10. If y = 1 is a source, show that dy/dt = f (y) must have at least two sinks between y = −10 and y = 10. (Can you say where they are located?)
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