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2.5 CONCAVITY
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Example: Consider the salary function S(t) shown in Table 2.15 and Figure 2.20, where t is time in years since being hired. Since the rate of change increases with time, the slope of the graph increases as t increases, so the graph bends upward. We say such graphs are concave up.
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Increasing and Decreasing Functions; Concavity
Increasing and concave down Decreasing and concave down Decreasing and concave up Increasing and concave up
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Summary: Increasing and Decreasing Functions; Concavity
• If f is a function whose rate of change increases, then the graph of f is concave up. That is, the graph bends upward. • If f is a function whose rate of change decreases, then the graph of f is concave down. That is, the graph bends downward. If a function has a constant rate of change, its graph is a line and it is neither concave up nor concave down.
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