Second derivative test
From Calculus
Statement
What this test is for
This test is a partial test (i.e., it may be inconclusive) for determining whether a given critical point for a function is a point of local minimum, point of local maximum, or neither.
What the test states
Suppose is a function and
is a point in the interior of the domain of
, i.e.,
is defined on some open interval containing
. Suppose, further, that
, i.e., the second derivative of
, exists at
. Suppose also that
, so
is a critical point for
. Then:
Hypothesis | Conclusion |
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The test is inconclusive. ![]() ![]() |