Difference between revisions of "Max Command"

Latest revision as of 13:43, 22 November 2023

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 (and no local minimum).; 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:

If you want the maximum of two functions f(x) and g(x) then you can define (f(x) + g(x) + abs(f(x) - g(x)))/2
See also Extremum Command, Min Command and Function Inspector Tool.

CAS Syntax

Max( <Function>, <Start x-Value>, <End x-Value> )

Unlike in the Algebra View, this syntax will give the maximum over the interval, including endpoints

Example:

Max(x^2,-1,2) yields the point (2,4)
Max(-x^2,-1,2) yields the point (0,0)

@@ Line 1: / Line 1: @@
-<noinclude>{{Manual Page|version=5.0}}</noinclude>
+<noinclude>{{Manual Page|version=5.0}}</noinclude>{{command|cas=true|algebra}}
-{{command|cas=true|algebra}}
+;Max( <List> )
-;Max[ <List> ]
 :Returns the maximum of the numbers within the list.
-:{{example| 1=<code><nowiki>Max[{-2, 12, -23, 17, 15}]</nowiki></code> yields ''17''.}}
+:{{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 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.}}
+:{{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.}}
+;Max( <Interval> )
-;Max[ <Interval> ]
 :Returns the upper bound of the interval.
-:{{example| 1=<code><nowiki>Max[2 < x < 3]</nowiki></code> yields ''3''.}}
+:{{example| 1=<code><nowiki>Max(2 < x < 3)</nowiki></code> yields ''3''.}}
 :{{note| 1=Open and closed intervals are treated the same.}}
+;Max( <Number>, <Number> )
-;Max[ <Number>, <Number> ]
 :Returns the maximum of the two given numbers.
-:{{example| 1=<code><nowiki>Max[12, 15]</nowiki></code> yields ''15''.}}
+:{{example| 1=<code><nowiki>Max(12, 15)</nowiki></code> 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 (and no local minimum).
-;Max[ <Function>, <Start x-Value>, <End x-Value> ]
+:{{note| 1=For polynomials you should use the [[Extremum Command]].}}
-: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(exp(x)x^2,-3,-1)</nowiki></code> creates the point (-2, 0.54134).}}
-:{{example| 1=<code><nowiki>Max[ x^3 + 2x^2 - 1, -2, 0]</nowiki></code> creates the point (-1.33, 0.19).}}
+;Max(<List of Data>, <List of Frequencies> )
-:{{note| 1=See also [[Extremum Command]], [[Min Command]] and [[Function Inspector Tool]].}}
+:Returns the maximum of the list of data with corresponding frequencies.
+:{{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.}}
-;Max[ <List of Data>, <List of Frequencies> ]
+{{note| 1=<div>
-:Returns the maximum of the list of data with corresponding frequencies.
+*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>
-:{{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.}}
+*See also [[Extremum Command]], [[Min Command]] and [[Function Inspector Tool]].</div>}}
 ==CAS Syntax==
-;Max[ <List> ]
+;Max( <Function>, <Start x-Value>, <End x-Value> )
-:Returns the maximum of the numbers within the list.
+:Unlike in the Algebra View, this syntax will give the maximum over the interval, including endpoints
-:{{example| 1=<code><nowiki>Max[{-2, 12, -23, 17, 15}]</nowiki></code> yields ''17''.}}
+:{{example|1=<div>
-:{{note| 1=See also [[Extremum Command]] and [[Min Command]].}}
+:*<code><nowiki>Max(x^2,-1,2)</nowiki></code> yields the point ''(2,4)''
+:*<code><nowiki>Max(-x^2,-1,2)</nowiki></code> yields the point ''(0,0)''
+</div>}}
-;Max[ <Number>, <Number> ]
-:Returns the maximum of the two given numbers.
-:{{example| 1=<code><nowiki>Max[12, 15]</nowiki></code> yields ''15''.}}

Difference between revisions of "Max Command"

Latest revision as of 13:43, 22 November 2023

Max

Command Categories (All commands)

CAS Syntax