The differentiable function f is defined for all real numbers. Information about its first derivative f′(x) is summarized in the following sign chart.
Interval Sign of f′(x)(−∞,−5)+(−5,−2)0 only at x=−5 and − elsewhere
(−2,3)+(3,7)−(7,∞)+
(a) Use the sign chart to determine the intervals on which f is increasing and the intervals on which f is decreasing.
(b) Identify the x–coordinates of all local extrema of f, and state whether each is a local maximum or a local minimum.
(c) Explain how the information in the sign chart supports each conclusion in parts (a) and (b).