Tangent - Maple Help

Student[Calculus1]

 Tangent
 find the tangent of an expression

 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 $\left[c-1,c+1\right]$ 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 $f\left(x\right)$.  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 $\left(c,f\left(c\right)\right)$ 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 $\left(c,f\left(c\right)\right)$ 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 $\left(c,f\left(c\right)\right)$, is displayed.
 pointoptions = list
 A list of options for the plot of the point $\left(c,f\left(c\right)\right)$. 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 $f\left(x\right)$ is plotted.  By default, the value is true.
 showpoint = true or false
 Whether the point $\left(c,f\left(c\right)\right)$ 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

 > $\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right):$
 > $\mathrm{Tangent}\left(\mathrm{sin}\left(x\right)+1,x=1\right)$
 ${x}{}{\mathrm{cos}}{}\left({1}\right){+}{\mathrm{sin}}{}\left({1}\right){+}{1}{-}{\mathrm{cos}}{}\left({1}\right)$ (1)
 > $\mathrm{Tangent}\left(\mathrm{sin}\left(x\right)+1,2,\mathrm{output}=\mathrm{slope}\right)$
 ${\mathrm{cos}}{}\left({2}\right)$ (2)
 > $\mathrm{Tangent}\left({x}^{3}-x,-0.432,\mathrm{view}=\left[-2..1,\mathrm{DEFAULT}\right],\mathrm{output}=\mathrm{plot}\right)$
 > $\mathrm{Tangent}\left(\mathrm{tan}\left(x\right),x=\frac{3}{2},\mathrm{output}=\mathrm{plot}\right)$
 > $\mathrm{Tangent}\left({x}^{2},x=1,\mathrm{output}=\mathrm{plot},\mathrm{showpoint}=\mathrm{false},\mathrm{tangentoptions}=\left[\mathrm{color}=\mathrm{green}\right]\right)$