AP Calculus ABmediummcq1 pt

A slope field is shown with segments sloping downward above the line y=2y = 2, upward below the line y=2y = 2, and horizontal exactly on y=2y = 2. Which differential equation is consistent with this field?

A.dydx=2y\dfrac{dy}{dx} = 2 - y
B.dydx=y2\dfrac{dy}{dx} = y - 2
C.dydx=2x\dfrac{dy}{dx} = 2 - x
D.dydx=y\dfrac{dy}{dx} = y

Explanation

Core Concept

For y>2y>2 the slope 2y2-y is negative, for y<2y<2 it is positive, and at y=2y=2 it is zero, exactly matching the description.

Correct Answer

Adydx=2y\dfrac{dy}{dx} = 2 - y

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