Difference between revisions of "Extremum Command"
From GeoGebra Manual
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{{command|function|US_version=Extremum|non-US_version=TurningPoint}} | {{command|function|US_version=Extremum|non-US_version=TurningPoint}} | ||
− | ;Extremum | + | ;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]].}} | :{{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 | + | ;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]].}} | :{{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 17:16, 7 October 2017
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.