In a slope field representing a first-order differential equation
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
In a slope field representing a first-order differential equation, which description best defines the “solution curve” that passes through a specific point (x0,y0)?
(a) The complete collection of all line segments in the slope field that lie on a horizontal line through (x0,y0).
(b) A polygonal path drawn through midpoints of slope segments starting at (x0,y0) using a fixed step size.
(c) A curve that is everywhere tangent to the line segments of the slope field and contains the point (x0,y0).
(d) A smooth curve that simply connects several selected slope segments but is not required to be tangent to them.