1. 2.5
CONCAVITY

2. 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.

3. Increasing and Decreasing Functions; Concavity
Increasing and concave down Decreasing and concave down
Decreasing and concave up Increasing and concave up

4. 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.