MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
A differentiable function f has first derivative f′. The following statements about f′ and f are often used when analyzing graphs.
(1) Explain what conclusion can be drawn about the behavior of f on the interval (a,b) based on statement (a). Include a clear verbal connection between the sign of f′ and the behavior of f. No numerical calculation is required.
(2) Explain what conclusion can be drawn about the point x=c on the graph of f based on statement (b). Be explicit about the type of critical point that occurs and why the sign change in f′ supports that conclusion.