Difference between revisions of "Extremum Command"

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{{command|function|US_version=Extremum|non-US_version=TurningPoint}}
 
{{command|function|US_version=Extremum|non-US_version=TurningPoint}}
 
;Extremum[ <Polynomial> ]:Yields all local extrema of the polynomial function as points on the function graph.
 
;Extremum[ <Polynomial> ]:Yields all local extrema of the polynomial function as points on the function graph.
:{{Example|1=<br><code>Extremum[x³ + 3x² - 2x + 1]</code> creates local extrema ''(0.29, 0.70)'' and ''(-2.29, 9.30)'' and shows them in the [[Graphics View]].}}  
+
:{{Example|1=<br><code><nowiki>Extremum[x³ + 3x² - 2x + 1]</nowiki></code> creates local extrema ''(0.29, 0.70)'' and ''(-2.29, 9.30)'' and shows them in the [[Graphics View]].}}  
 
;Extremum[ <Function>, <Start x-Value>, <End x-Value> ]:Calculates (numerically) the extremum of the function in the open interval ( <Start x-Value>, <End x-Value> ).
 
;Extremum[ <Function>, <Start x-Value>, <End x-Value> ]:Calculates (numerically) the extremum of the function in the open interval ( <Start x-Value>, <End x-Value> ).
:{{Example|1=<br><code>Extremum[(x⁴ - 3x³ - 4x² + 4) / 2, 0, 5]</code> creates local extremum ''(2.93, -16.05)'' in the given interval and shows it in the [[Graphics View]].}}
+
:{{Example|1=<br><code><nowiki>Extremum[(x⁴ - 3x³ - 4x² + 4) / 2, 0, 5]</nowiki></code> creates local extremum ''(2.93, -16.05)'' in the given interval and shows it in the [[Graphics View]].}}
 
:{{Note|1=The function should be continuous in [ <Start x-Value>, <End x-Value> ], otherwise false extrema near discontinuity might be calculated.}}
 
:{{Note|1=The function should be continuous in [ <Start x-Value>, <End x-Value> ], otherwise false extrema near discontinuity might be calculated.}}

Revision as of 09:33, 24 May 2013


Extremum[ <Polynomial> ]
Yields all local extrema of the polynomial function as points on the function graph.
Example:
Extremum[x³ + 3x² - 2x + 1] creates local extrema (0.29, 0.70) and (-2.29, 9.30) and shows them in the Graphics View.
Extremum[ <Function>, <Start x-Value>, <End x-Value> ]
Calculates (numerically) the extremum of the function in the open interval ( <Start x-Value>, <End x-Value> ).
Example:
Extremum[(x⁴ - 3x³ - 4x² + 4) / 2, 0, 5] creates local extremum (2.93, -16.05) in the given interval and shows it in the Graphics View.
Note: The function should be continuous in [ <Start x-Value>, <End x-Value> ], otherwise false extrema near discontinuity might be calculated.
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