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At a critical point c where f'(c) = 0, if f''(c) > 0, then c is a:
ALocal MINIMUM (concave up at c)
BLocal MAXIMUM (concave down)
CInflection point (no extremum)
DSaddle point (multivariable)
Answer & Solution
Correct answer: A. Local MINIMUM (concave up at c)
Second derivative test: f''(c) > 0 → concave UP → c is a local MINIMUM. f''(c) < 0 → concave DOWN → local MAXIMUM. f''(c) = 0 → test fails, use first-derivative test.
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