How to Find Concavity?

Find the second derivative, (f”(x))

Determine where (f”(x) > 0)

The graph is concave up on intervals where (f”(x) > 0)

Determine where (f”(x) < 0)

The graph is concave down on intervals where (f”(x) < 0)

Find where (f”(x) = 0) or is undefined

Check for sign changes of (f”(x)) at those points

Points where (f”(x)) changes sign are inflection points

State the intervals of concavity using interval notation

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