Difference between revisions of "Math 22 Extrema and First Derivative Test"

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If <math>f</math> has a relative minimum or relative maximum at <math>x=c</math>, then <math>c</math> is a critical number of <math>f</math>. That is, either <math>f'(c)=0</math> or <math>f'(c)</math> is undefined.
 
If <math>f</math> has a relative minimum or relative maximum at <math>x=c</math>, then <math>c</math> is a critical number of <math>f</math>. That is, either <math>f'(c)=0</math> or <math>f'(c)</math> is undefined.
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[[File:Relative extrema.png]]
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==The First-Derivative Test==
 
==The First-Derivative Test==
  

Revision as of 08:33, 30 July 2020

Relative Extrema

 Let  be a function defined at .
 1.  is a relative maximum of  when there exists an interval  containing  such that  for all  in .
 2.  is a relative minimum of  when there exists an interval  containing  such that  for all  in .

If has a relative minimum or relative maximum at , then is a critical number of . That is, either or is undefined.

Relative extrema.png

The First-Derivative Test

Absolute Extrema

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