MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Four smooth curves A, B, C, and D are drawn on the same coordinate plane.
• Curve A has a local maximum at x=−2 and a point of inflection at x=1.
• Curve B crosses the x-axis at x=−2 and x=1.
• Curve C crosses the x-axis only at x=1 and changes from negative to positive there.
• Curve D remains strictly positive for all x shown and has no relative extrema at x=−2 or x=1.
Exactly three of these curves belong to the family consisting of a function, its first derivative, and its second derivative. Which curve does NOT belong to that family? Give the letter.