A slope field for a differential equation displays the following pattern: along the…
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A slope field for a differential equation displays the following pattern: along the horizontal line y=1 the slope elements are zero; above that line the slope elements are negative, and below that line they are positive. Which statement is most consistent with the qualitative behavior of any solution that starts at the point (0,3)?
(a) The solution increases away from y=1 and grows without bound as x increases.
(b) The solution remains constant at y=3 for all x.
(c) The solution decreases and approaches y=1 as x increases.
(d) The solution decreases and approaches y=0 as x increases.