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Student[Calculus1][CriticalPoints] - find the critical points of an expression

Calling Sequence

CriticalPoints(f(x), x, opts)

CriticalPoints(f(x), x = a..b, opts)

CriticalPoints(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 critical points

opts

-

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

Description

• 

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

• 

The CriticalPoints(f(x), x = a..b) command returns all critical 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.

• 

A critical point is defined as any point at which the derivative is either zero or does not exist.

• 

If the expression has an infinite number of critical points, a warning message and sample critical 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 critical 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]:

CriticalPoints3x2x

16

(1)

CriticalPoints3x55x3+3,x

1,0,1

(2)

CriticalPoints2x3+5x24x

2,13

(3)

CriticalPoints2x3+5x24x,x=0..1

13

(4)

CriticalPointsx23x+1x,x

1,1

(5)

CriticalPointsx23x+1x,x,numeric

1.000000000,1.000000000

(6)

See Also

Student, Student[Calculus1], Student[Calculus1][Asymptotes], Student[Calculus1][CurveAnalysisTutor], Student[Calculus1][ExtremePoints], Student[Calculus1][FunctionChart], Student[Calculus1][InflectionPoints], Student[Calculus1][Roots]


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