MATHEMATICS · Subjective · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
Three twice-differentiable curves labeled A, B, and C each pass through the point (1,0). At x=1:
• Curve A has a horizontal tangent.
• Curve B crosses the x-axis with positive slope.
• Curve C is increasing and concave up.
If the curves represent a function f, its first derivative f′, and its second derivative f′′ in some order, which curve must correspond to f′? Give the letter of the curve.