Extreme Points - Maple Help

Student[Calculus1]

 ExtremePoints
 find the extreme points of an expression

 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

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right):$
 > $\mathrm{ExtremePoints}\left(3{x}^{2}-x\right)$
 $\left[\frac{{1}}{{6}}\right]$ (1)
 > $\mathrm{ExtremePoints}\left(3{x}^{5}-5{x}^{3}+3,x\right)$
 $\left[{-1}{,}{1}\right]$ (2)
 > $\mathrm{ExtremePoints}\left(2{x}^{3}+5{x}^{2}-4x\right)$
 $\left[{-2}{,}\frac{{1}}{{3}}\right]$ (3)
 > $\mathrm{ExtremePoints}\left(2{x}^{3}+5{x}^{2}-4x,x=0..1\right)$
 $\left[{0}{,}\frac{{1}}{{3}}{,}{1}\right]$ (4)
 > $\mathrm{ExtremePoints}\left(\frac{{x}^{2}-3x+1}{x},x\right)$
 $\left[{-1}{,}{1}\right]$ (5)
 > $\mathrm{ExtremePoints}\left(\frac{{x}^{2}-3x+1}{x},x,\mathrm{numeric}\right)$
 $\left[{-10.}{,}{-1.000000000}{,}{1.000000000}{,}{10.}\right]$ (6)