The differential equation is used to create a slope field

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

Problem

The differential equation dydx=y(2−y)\dfrac{dy}{dx}=y(2-y) is used to create a slope field. Which statement best describes the appearance of the slope field along the horizontal line y=2y=2? (a) The line segments tilt upward because dydx=2\dfrac{dy}{dx}=2. (b) No line segments are drawn along y=2y=2 since it is an equilibrium solution. (c) The line segments are horizontal because dydx=0\dfrac{dy}{dx}=0. (d) The line segments tilt downward with slope −2-2.

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