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Student[Calculus1]

  

Tangent

  

find the tangent of an expression

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

Tangent(f(x), x = c, a..b, opts)

Tangent(f(x), c, a..b, opts)

Parameters

f(x)

-

algebraic expression in variable 'x'

x

-

name; specify the independent variable

c

-

algebraic expression; specify the point of tangency

a, b

-

algebraic expressions; specify the plot range

opts

-

equation(s) of the form option=value where option is one of functionoptions, output, pointoptions, showfunction, showpoint, showtangent, tangentoptions, or Student plot options; specify plot options

Description

• 

The Tangent(f(x), x=c, a..b) command returns the equation of the line tangent to the graph of f(x) at the point c. By using options, you can specify that the command returns a plot or the slope of the tangent line instead.

• 

The optional argument a..b gives the range of the plot.  If no range is given, the interval c1,c+1 is used.

• 

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

• 

The opts argument can contain any of the Student plot options or any of the following equations that (excluding output) set plot options.

  

 

  

functionoptions = list

  

A list of options for the plot of the expression fx.  By default, the expression is plotted as a solid red line. For more information on plot options, see plot/options.

  

 

  

output = line, slope, or plot

  

This option controls the return value of the function.

– 

output = line specifies that the equation of the tangent line passing through the point c,fc is returned. Plotting options are ignored if output = line.  This is the default.

– 

output = slope specifies that the slope of the tangent at the point c,fc is returned. Plotting options are ignored if output = slope.

– 

output = plot specifies that a plot, which shows the expression and the tangent at the point c,fc, is displayed.

  

 

  

pointoptions = list

  

A list of options for the plot of the point c,fc. By default, this point is plotted as a blue circle. For more information on plot options, see plot/options.

  

 

  

showfunction = true or false

  

Whether the expression fx is plotted.  By default, the value is true.

  

 

  

showpoint = true or false

  

Whether the point c,fc is plotted. By default, the value is true.

  

 

  

showtangent = true or false

  

Whether the tangent line is plotted. By default, the value is true.

  

 

  

tangentoptions = list

  

A list of options for the plot of the tangent line. By default, this is plotted as a solid blue line. For more information on plot options, see plot/options.

  

 

  

caption = anything

  

A caption for the plot.

  

The default caption is constructed from the parameters and the command options. caption = "" disables the default caption. For more information about specifying a caption, see plot/typesetting.

Examples

withStudent[Calculus1]:

Tangentsinx+1,x=1

xcos1+sin1+1cos1

(1)

Tangentsinx+1,2,output=slope

cos2

(2)

Tangentx3x,0.432,view=2..1,DEFAULT,output=plot

Tangenttanx,x=32,output=plot

Tangentx2,x=1,output=plot,showpoint=false,tangentoptions=color=green

See Also

plot/options

plot/typesetting

Student

Student plot options

Student[Calculus1]

Student[Calculus1][DerivativePlot]

Student[Calculus1][TangentSecantTutor]

Student[Calculus1][TangentTutor]

Student[Calculus1][VisualizationOverview]

 


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