Difference between revisions of "Max Command"

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(added example for functions)
(same as Min command for functions method (numerically))
(12 intermediate revisions by 7 users not shown)
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<noinclude>{{Manual Page|version=4.2}}</noinclude>
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<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|algebra}}
{{command|cas=true|algebra}}
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;Max( <List> )
;Max[ <Number>, <Number> ]
 
:Returns the maximum of the two given numbers.
 
:{{example| 1=<code><nowiki>Max[12, 15]</nowiki></code> yields ''15''.}}
 
;Max[ <List of Numbers> ]
 
 
:Returns the maximum of the numbers within the list.
 
:Returns the maximum of the numbers within the list.
:{{example| 1=<code><nowiki>Max[{-2, 12, -23, 17, 15}]</nowiki></code> yields ''17''.}}
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:{{example| 1=<code><nowiki>Max({-2, 12, -23, 17, 15})</nowiki></code> yields ''17''.}}
:{{note| 1=If the input consists of non-numeric objects, then ''Max''[] considers the numbers associated with those objects. For example, ''Max''[''List of Segments''] will yield the maximum segment length.}}
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:{{note| 1=If the input consists of non-numeric objects, then this command considers the numbers associated with those objects. If you have a list of segments for example, the command ''Max( &lt;List> )'' will yield the maximum segment length.}}
 
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;Max( <Interval> )
;Max[ <Function>, <left-x>, <right-x> ]
 
:Calculates the maximum point of the function in the given interval. The function should be continuous and have only one ''local'' maximum point in the interval.
 
:{{example| 1=<code><nowiki>Max[ x^3 + 2x^2 - 1, -2, 0]</nowiki></code> creates the point (-1.33, 0.19).}}
 
;Max[ <Interval> ]
 
 
:Returns the upper bound of the interval.
 
:Returns the upper bound of the interval.
:{{example| 1=<code><nowiki>Max[2 < x < 3]</nowiki></code> yields ''3''.}}
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:{{example| 1=<code><nowiki>Max(2 < x < 3)</nowiki></code> yields ''3''.}}
 
:{{note| 1=Open and closed intervals are treated the same.}}
 
:{{note| 1=Open and closed intervals are treated the same.}}
{{note| 1=See also [[Extremum Command]], [[Min Command]] and [[Function Inspector Tool]].}}
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;Max( <Number>, <Number> )
==CAS Syntax==
 
;Max[ <Number>, <Number> ]
 
 
:Returns the maximum of the two given numbers.
 
:Returns the maximum of the two given numbers.
:{{example| 1=<code><nowiki>Max[12, 15]</nowiki></code> yields ''15''.}}
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:{{example| 1=<code><nowiki>Max(12, 15)</nowiki></code> yields ''15''.}}
;Max[ <List of Numbers> ]
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;Max( <Function>, <Start x-Value>, <End x-Value> )
:Returns the maximum of the numbers within the list.
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:Calculates (numerically) the '''local''' maximum point of the function in the given interval. The function should be continuous and have only one ''local'' maximum point in the interval.
:{{example| 1=<code><nowiki>Max[{-2, 12, -23, 17, 15}]</nowiki></code> yields ''17''.}}
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:{{note| 1=For polynomials you should use the [[Extremum Command]].}}
{{note| 1=See also [[Extremum Command]] and [[Min Command]].}}
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:{{example| 1=<code><nowiki>Max(exp(x)x^2,-3,-1)</nowiki></code> creates the point (-2, 0.54134).}}
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;Max(<List of Data>, <List of Frequencies> )
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:Returns the maximum of the list of data with corresponding frequencies.  
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:{{example| 1=<code><nowiki>Max({1, 2, 3, 4, 5}, {5, 3, 4, 2, 0})</nowiki></code> yields 4, the highest number of the list whose frequency is greater than 0.}}
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{{note| 1=<div>
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*If you want the maximum of two functions <code>f(x)</code> and <code>g(x)</code> then you can define <code>(f(x) + g(x) + abs(f(x) - g(x)))/2</code>
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*See also [[Extremum Command]], [[Min Command]] and [[Function Inspector Tool]].</div>}}

Revision as of 08:09, 25 October 2019


Max( <List> )
Returns the maximum of the numbers within the list.
Example: Max({-2, 12, -23, 17, 15}) yields 17.
Note: If the input consists of non-numeric objects, then this command considers the numbers associated with those objects. If you have a list of segments for example, the command Max( <List> ) will yield the maximum segment length.
Max( <Interval> )
Returns the upper bound of the interval.
Example: Max(2 < x < 3) yields 3.
Note: Open and closed intervals are treated the same.
Max( <Number>, <Number> )
Returns the maximum of the two given numbers.
Example: Max(12, 15) yields 15.
Max( <Function>, <Start x-Value>, <End x-Value> )
Calculates (numerically) the local maximum point of the function in the given interval. The function should be continuous and have only one local maximum point in the interval.
Note: For polynomials you should use the Extremum Command.
Example: Max(exp(x)x^2,-3,-1) creates the point (-2, 0.54134).
Max(<List of Data>, <List of Frequencies> )
Returns the maximum of the list of data with corresponding frequencies.
Example: Max({1, 2, 3, 4, 5}, {5, 3, 4, 2, 0}) yields 4, the highest number of the list whose frequency is greater than 0.


Note:
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