A slope field for an unknown differential equation shows that at every point on the…
MATHEMATICS · Single correct · AP · Calculus AB · Differential Equations · Differential Equations
Problem
A slope field for an unknown differential equation shows that at every point on the vertical line x=2 the slope elements are horizontal. Immediately to the left of x=2 the line elements tilt upward (positive slope), while immediately to the right of x=2 they tilt downward (negative slope). For a solution curve that passes through the point (2,1), which statement best describes the behavior of the solution at x=2?
(a) The slope of the solution is undefined at x=2. (vertical tangent)
(b) The solution attains a relative maximum in y at x=2.
(c) The solution attains a relative minimum in y at x=2.
(d) The solution has an inflection point at x=2 but neither a maximum nor a minimum.