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Student[Calculus1]

  

ExtremePoints

  

find the extreme points of an expression

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

ExtremePoints(f(x), x, opts)

ExtremePoints(f(x), x = a..b, opts)

ExtremePoints(f(x), a..b, opts)

Parameters

f(x)

-

algebraic expression in variable 'x'

x

-

name; specify the independent variable

a, b

-

algebraic expressions; specify restricted interval for extreme points

opts

-

equation(s) of the form numeric=true or false; specify computation options

Description

• 

The ExtremePoints(f(x), x) command returns all extreme points of f(x) as a list of values.

• 

The ExtremePoints(f(x), x = a..b) command returns all extreme points of f(x) in the interval [a,b] as a list of values.

• 

If the independent variable can be uniquely determined from the expression, the parameter x need not be included in the calling sequence.

• 

An extreme point is defined as any point which is a local minimum or maximum, which includes any finite end points.

• 

If the expression has an infinite number of extreme points, a warning message and sample extreme points are returned.

• 

The opts argument can contain the following equation that sets computation options.

  

 

  

numeric = true or false

  

Whether to use numeric methods (using floating-point computations) to find the extreme points of the expression. If this option is set to true, the points a and b must be finite and are set to 10 and 10 if they are not provided. By default, the value is false.

Examples

withStudent[Calculus1]:

ExtremePoints3x2x

16

(1)

ExtremePoints3x55x3+3,x

1,1

(2)

ExtremePoints2x3+5x24x

2,13

(3)

ExtremePoints2x3+5x24x,x=0..1

0,13,1

(4)

ExtremePointsx23x+1x,x

1,1

(5)

ExtremePointsx23x+1x,x,numeric

10.,1.000000000,1.000000000,10.

(6)

See Also

Student

Student[Calculus1]

Student[Calculus1][Asymptotes]

Student[Calculus1][CriticalPoints]

Student[Calculus1][CurveAnalysisTutor]

Student[Calculus1][FunctionChart]

Student[Calculus1][InflectionPoints]

Student[Calculus1][Roots]

 


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