A slope field for shows horizontal tangents at

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

Problem

A slope field for

\dfrac{dy}{dt}=g(y)

shows horizontal tangents at

y=2

. Just above

y=2

the arrows point downward, and just below

y=2

the arrows point upward. Which of the following best describes the nature of the equilibrium solution

y=2

? (a) It is neutrally stable because nearby solution curves remain at a constant distance from

y=2

. (b) It is unstable because solution curves on both sides move away from

y=2

. (c) It is stable because solution curves on both sides move toward

y=2

. (d) It is semi-stable because solution curves move toward

y=2

from below and away from it from above.