At a critical point c where f'(c) = 0, if f''(c) 0, then c is a:

Question

At a critical point c where f'(c) = 0, if f''(c) > 0, then c is a:

Accepted 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.

Answer

Local MAXIMUM (concave down)

Answer

Inflection point (no extremum)

Answer

Saddle point (multivariable)

At a critical point c where f'(c) = 0, if f''(c) > 0, then c is a:

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