Difference between revisions of "Extremum Command"
From GeoGebra Manual
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| − | <noinclude>{{Manual Page}} | + | <noinclude>{{Manual Page|version=5.0}}</noinclude> |
| − | + | {{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><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> ). | ||
| + | :{{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.}} | ||
Revision as of 10:19, 5 August 2015
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This command differs among variants of English:
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- 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.
