Consider the differential equation. A detailed direction field is not needed. Find the solutions that are constant, for all
(the equilibrium solutions). In what regions are solutions increasing? Decreasing?y'(t) = y(y + 2)(6 - y)
A. y = -2, y = 6; increasing for -2 < y < 6; decreasing for y < -2, y > 6
B. y = 0, y = -2, y = 6; increasing for -2 < y < 0; decreasing for y < -2, y > 0
C. y = 0, y = -2, y = 6; increasing for y < -2, 0 < y < 6; decreasing for -2 < y < 0, y > 6
D. y = -2, y = 6; increasing for y < -2, 0 < y < 6; decreasing for -2 < y < 0, y > 6
Answer: C
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