17Calculus Derivatives - Concavity

17Calculus

Concavity

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.

PatrickJMT - Concavity [10min-22secs]

video by PatrickJMT

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