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In Section 3.2, we are given the official definition of relative extrema and taught to use First-Derivative Test to identify relative extrema. In Section 3.3,
In Section 3.2, we are given the official definition of relative extrema and taught to use First-Derivative Test to identify relative extrema. In Section 3.3, we are given the definition of concavity and taught to use Second-Derivative Test to find relative extrema as well. Please compare the pros and cons of finding extrema using First-Derivative Test and Second-Derivative Tests. Please also comment on why when f"(c) > 0, then f(c) is a relative minimum and when f"(c) < 0, then f(c) is a relative maximum.
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