Calculus › Section D · Applications of derivatives › Topic D.4
Concavity and the second derivative test
A curve can rise while steepening, or rise while flattening. Concavity is the study of how a graph bends, and the second derivative answers it as crisply as the first derivative answered rise and fall.
In this topic
- Two ways to climb
- Concavity, defined by the tangent slopes
- The second derivative decides
- Inflection points
- Worked example: two inflection points
- The second derivative test for extrema
- Worked example: the test on our cubic
- The point of diminishing returns
- Common mistakes to avoid
- Key takeaways
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Standards: 5