Difference between revisions of "Extremum Command"

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<noinclude>{{Manual Page|version=4.0}}[[Category:Manual (official)|{{PAGENAME}}]]</noinclude>
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<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.
 
;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 points - <code>(0.29, 0.696)</code> and <code>(-2.3, 9.3)</code> -  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 ''f''>, <left-x>, <right-x> ]:Calculates (numerically) the extremum of ''f''  in the open interval ( <code><left-x>, <right-x></code> )
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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> ).
:{{Note|1=Function ''f'' should be continuous in [ <left-x>, <right-x> ], otherwise false extremums near discontinuity might be calculated.}}
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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]].}}
:{{Example|1=<br><code>Extremo[(x⁴ - 3x³ - 4x² + 4) / 2, x(X_i), x(X_f)]</code> creates each local extrema point in the given interval and shows it in the [[Graphics View]].}}
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:{{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 09:19, 5 August 2015


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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