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.