A slope field has the following property: at every point with the line segments have…

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

Problem

A slope field has the following property: at every point with

x=0

the line segments have slope

-1

; at every point with

x=1

the segments are horizontal; and at every point with

x=2

the segments have slope

1

. Which differential equation is most consistent with these observations? (a)

\dfrac{dy}{dx}=1-x

(b)

\dfrac{dy}{dx}=x(x-1)

(c)

\dfrac{dy}{dx}=x-1

(d)

\dfrac{dy}{dx}=2-x