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

Revision as of 08:31, 30 July 2020

Relative Extrema

 Let  $f$  be a function defined at  $c$ .
 1.  $f(c)$  is a relative maximum of  $f$  when there exists an interval  $(a,b)$  containing  $c$  such that  $f(x)\leq f(c)$  for all  $x$  in  $(a,b)$ .
 2.  $f(c)$  is a relative minimum of  $f$  when there exists an interval  $(a,b)$  containing  $c$  such that  $f(x)\geq f(c)$  for all  $x$  in  $(a,b)$ .

If $f$ has a relative minimum or relative maximum at $x=c$ , then $c$ is a critical number of $f$ . That is, either $f'(c)=0$ or $f'(c)$ is undefined.

The First-Derivative Test

Absolute Extrema

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@@ Line 1: / Line 1: @@
+==Relative Extrema==
+  Let <math>f</math> be a function defined at <math>c</math>.
+. <math>f(c)</math> is a relative maximum of <math>f</math> when there exists an interval <math>(a,b)</math> containing <math>c</math> such that <math>f(x)\le f(c)</math> for all <math>x</math> in <math>(a,b)</math>.
+. <math>f(c)</math> is a relative minimum of <math>f</math> when there exists an interval <math>(a,b)</math> containing <math>c</math> such that <math>f(x)\ge f(c)</math> for all <math>x</math> in <math>(a,b)</math>.
+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.
+==The First-Derivative Test==
+==Absolute Extrema==
 The page is under Construction

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

Revision as of 08:31, 30 July 2020

Relative Extrema

The First-Derivative Test

Absolute Extrema

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