The slope field for the differential equation contains two equilibrium solution curves

MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations

Problem

The slope field for the differential equation dydx=y(3−y)\dfrac{dy}{dx}=y(3-y) contains two equilibrium solution curves. Which yy-value corresponds to a stable equilibrium indicated by horizontal segments toward which nearby solution curves tend as xx increases? (a) y=0y=0 (b) y=3y=3 (c) y=1.5y=1.5 (d) y=−3y=-3

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