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AP Calculus AB/BC
Unit 5 – Analytical Applications of Differentiation
Topic 5.7
The Second Derivative Test is used to analyze the concavity of a function and determine whether a critical point is a relative minimum, relative maximum, or neither. This test is based on the principle that:
The second derivative is always negative for a relative maximum and always positive for a relative minimum.
The second derivative changes sign at a relative extremum.
The second derivative is always positive for a relative maximum and always negative for a relative minimum.
The first derivative is always positive for a relative maximum and always negative for a relative minimum.
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AP Calculus AB/BC - 5.7 Using the Second Derivative Test to Determine Extrema
Key terms
Concavity
Critical Point
Relative Maximum
Relative Minimum
Second Derivative Test
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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
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