7.7.2 Extrema using Second Derivative Test
Chapter 1: Chapter 7 · MATHEMATICS-VOLUME 2 · EN medium
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The Second Derivative Test: The Second Derivative Test relates the concepts of critical points, extreme values, and concavity to give a very useful tool for determining whether a critical point on the graph of a function is a relative minimum or maximum. Theorem . (The Second Derivative Test) Suppose that c is a critical point at which ′ c ( ) , that ′ f ( ) exists in a neighborhood of c , and that f ( ) c exists. Then f has a relative maximum value at c if ′′ c ( ) and a relative minimum value at c if ′′ > c ( ) . If ′′ c ( ) , the test is not informative. . . .
📖 Class 12 Mathematics English Volume 2 2025 Edition www.tntextbooks.in · Page 46
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The Second Derivative Test: The Second Derivative Test relates the concepts of critical points, extreme values, and concavity to give a very useful tool for determining whether a critical point on the graph of a function is a relative minimum or maximum. Theorem . (The Second Derivative Test) Suppose that c is a critical point at which ′ c ( ) , that ′ f ( ) exists in a neighborhood of c , and that f ( ) c exists. Then f has a relative maximum value at c if ′′ c ( ) and a relative minimum value at c if ′′ > c ( ) .
If ′′ c ( ) , the test is not informative. . . .
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