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Second derivative test

135 bytes added, 15:39, 2 May 2012
What the test says
{| class="sortable" border="1"
! Hypothesis on <math>f'(c)</math> !! Hypothesis on <math>f''(c)</math>!! Conclusion
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| <math>f'(c) =0</math> || <math>f''(c) < 0</math> || <math>f</math> attains a local maximum value at <math>c</math> (the ''value'' is <math>f(c)</math>)
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| <math>f'(c) = 0</math> || <math>f''(c) > 0</math> || <math>f</math> attains a local minimum value at <math>c</math> (the ''value'' is <math>f(c)</math>)
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| <math>f'(c) = 0</math> || <math>f''(c) = 0</math> || The test is inconclusive. <math>f</math> may attain a local maximum value, a local minimum value, have a [[point of inflection]], or have some different behavior at the point <math>c</math>.
|}
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