First Derivative Test vs Second Derivative Test for Local Extrema
Key Questions
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Since you are asking for the difference, I assume that you are familiar with how each test works. The biggest difference is that the first derivative test always determines whether a function has a local maximum, a local minimum, or neither; however, the second derivative test fails to yield a conclusion when
#y''# is zero at a critical value. If that is the case, you will have to apply the first derivative test to draw a conclusion.
Questions
Graphing with the Second Derivative
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Relationship between First and Second Derivatives of a Function
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Analyzing Concavity of a Function
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Notation for the Second Derivative
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Determining Points of Inflection for a Function
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First Derivative Test vs Second Derivative Test for Local Extrema
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The special case of x⁴
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Critical Points of Inflection
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Application of the Second Derivative (Acceleration)
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Examples of Curve Sketching