Difference between revisions of "Extremum Command"
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− | <noinclude>{{Manual Page | + | <noinclude>{{Manual Page|version=5.0}}</noinclude> |
− | {{command|function}} | + | {{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. |
+ | :{{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.}} | ||
− | ; Extremum | + | ==CAS Syntax== |
+ | ;Extremum( <Function> ) | ||
+ | :Will attempt to return all local extrema of the function (which should be continuous and differentiable) | ||
+ | |||
+ | :{{Example|1=<code><nowiki>Extremum(x³ + 3x² - 2x + 1)</nowiki></code> creates a list of the points and plots them ''<math> \left\{ \left(\frac{-\sqrt{15} - 3}{3}, \frac{10 \; \sqrt{15} + 45}{9} \right), \left(\frac{\sqrt{15} - 3}{3}, \frac{-10 \; \sqrt{15} + 45}{9} \right) \right\}</math>''.}} | ||
+ | |||
+ | :{{Example|1=<code><nowiki>Assume(0 < x < 20, Extremum(15/2 * sin( 2/15*pi * x) + 56/5))</nowiki></code> yields the local turning points in the range given ''<math> \left\{ \left(\frac{15}{4}, \frac{187}{10} \right), \left(\frac{45}{4}, \frac{37}{10} \right), \left(\frac{75}{4}, \frac{187}{10} \right) \right\} </math>''.}} |
Latest revision as of 14:52, 15 October 2023
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.
CAS Syntax
- Extremum( <Function> )
- Will attempt to return all local extrema of the function (which should be continuous and differentiable)
- Example:
Extremum(x³ + 3x² - 2x + 1)
creates a list of the points and plots them \left\{ \left(\frac{-\sqrt{15} - 3}{3}, \frac{10 \; \sqrt{15} + 45}{9} \right), \left(\frac{\sqrt{15} - 3}{3}, \frac{-10 \; \sqrt{15} + 45}{9} \right) \right\}.
- Example:
Assume(0 < x < 20, Extremum(15/2 * sin( 2/15*pi * x) + 56/5))
yields the local turning points in the range given \left\{ \left(\frac{15}{4}, \frac{187}{10} \right), \left(\frac{45}{4}, \frac{37}{10} \right), \left(\frac{75}{4}, \frac{187}{10} \right) \right\} .