In a slope field for a first-order differential equation

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

Problem

In a slope field for a first-order differential equation dydx=f(x,y)\dfrac{dy}{dx}=f(x,y), what does the short line segment drawn at a point (x0,y0)(x_0, y_0) represent? (a) The slope of a line perpendicular to the solution curve at (x0,y0)(x_0, y_0), i.e., −1f(x0,y0)-\dfrac{1}{f(x_0, y_0)}.},{ (b) The slope of the tangent line to the solution curve that passes through (x0,y0)(x_0, y_0).},{ (c) The value of the second derivative d2ydx2\dfrac{d^2y}{dx^2} at (x0,y0)(x_0, y_0).},{ (d) The magnitude of the slope only, ∣f(x0,y0)∣|f(x_0, y_0)|, regardless of sign.

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