Difference between revisions of "Extremum Command"

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<noinclude>{{Manual Page|version=5.0}}</noinclude>
 
<noinclude>{{Manual Page|version=5.0}}</noinclude>
 
{{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.
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;Extremum( <Polynomial> ):Yields all local extrema of the polynomial function as points on the function graph.
:{{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]].}}  
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:{{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 [[File:Menu view graphics.svg|link=|16px]] [[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> ).
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;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><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]].}}
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:{{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 [[File:Menu view graphics.svg|link=|16px]] [[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 08:05, 9 October 2017


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 Menu view graphics.svg 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 Menu view graphics.svg 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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