A slope field for a differential equation has the following pattern along the…
MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A slope field for a differential equation has the following pattern along the vertical line x=−2:
• For x<−2 the line segments slope downward as x increases.
• On x=−2 the line segments are horizontal.
• For x>−2 the line segments slope upward as x increases.
Which of the following best describes the behavior of any non-constant solution curve at x=−2?
(a) The curve is strictly increasing at x=−2 because the derivative is positive there.
(b) The curve attains a relative maximum at x=−2 because it changes from increasing to decreasing.
(c) The curve attains a relative minimum at x=−2 because it changes from decreasing to increasing.
(d) The curve has a point of inflection at x=−2 because the derivative changes sign there.