The Second-Derivative Test for Local Max (M) and Min (m)

• If f’(p) = 0 and f’’(p) > 0 then f has a local minimum at p.

• If f’(p) = 0 and f’’(p) < 0 then f has a local maximum at p.

• if f’(p) = 0 and f’’(p) = 0 then the test tells nothing.

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