Concavity
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Concavity relates to how the graph is curving, either upward or downward. If a graph is curving upward, then it looks like a cup and it could hold water. The graph of \(y=x^2\) is concave upward.
If the graph is curving downward, then it looks like an arched roof and could keep you dry you in the rain. The graph of \(y=-x^2\) is concave downward.
This plot shows several examples of concavity to help you get a feel for what they look like.
The concept of concavity parallels increasing and decreasing intervals. We learned that increasing and decreasing sections of a function change only at critical points. Similarly, concavity is related to the second derivative and changes only at inflection points.
Here is a quick video clip explaining this idea again.
video by PatrickJMT |
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