Consider the slope field for

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

Problem

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

. A student begins to sketch the solution curve that passes through the initial point

(1,0)

. Which statement best describes the immediate behavior of this curve as

x

increases from

1

? (a) The curve moves upward because the indicated slopes are positive at

(1,0)

. (b) The curve is horizontal because the indicated slope is zero at

(1,0)

. (c) The curve moves downward because the indicated slopes are negative at

(1,0)

. (d) The curve is vertical because

\dfrac{dy}{dx}

is undefined at

(1,0)