MATHEMATICS · Multi-part · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation
Problem
The graph of g, the derivative of a twice–differentiable function f, is described below.
• For x<−2, the graph of g lies strictly below the x–axis.
• At x=−2, the graph of g intersects the x–axis and then remains strictly above the axis on the open interval (−2,1).
• At x=1, the graph of g again intersects the x–axis and then remains strictly below the axis for all x>1.
No other x–intercepts or discontinuities of g occur.
Answer the following questions about f.
(a) Identify all critical numbers of f. Explain why each value qualifies.
(b) Determine the open intervals on which f is increasing and the open intervals on which f is decreasing.
(c) Classify each critical number as the x–coordinate of a local maximum, a local minimum, or neither, and justify your classification.