Concavity and Inflection Points

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This skill is located in Section 3.3. See Concavity and Inflection Points.

Quick Reference

Concavity

• $f''(x) > 0$: Concave up (cup shape, tangent lines below curve)
• $f''(x) < 0$: Concave down (cap shape, tangent lines above curve)

Inflection Points

A point where the concavity changes. At an inflection point $c$:

• $f''(c) = 0$ or $f''(c)$ doesn’t exist
• $f''$ changes sign at $c$

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