In a slope field for the first-order differential equation

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

Problem

\dfrac{dy}{dx}=f(x,y)

, what does each short line segment drawn at a lattice point

(x_0, y_0)

represent? (a) The exact value

y_0

of the solution at

(x_0,y_0)

(b) The value of the second derivative

\displaystyle \frac{d^{2}y}{dx^{2}}

(x_0,y_0)

f(x_0,y_0)

of the solution curve through

(x_0,y_0)

(d) The direction of the gradient vector

\nabla f(x_0,y_0)

at the point