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.

$\mathrm{with}\left(\mathrm{Student}\left[\mathrm{Calculus1}\right]\right)\:$

$\mathrm{Tangent}\left(\sin \left(x\right)+1\,x=1\right)$

$x\cos \left(1\right)+\sin \left(1\right)+1-\cos \left(1\right)$

$\mathrm{Tangent}\left(\sin \left(x\right)+1\,2\,\mathrm{output}=\mathrm{slope}\right)$

$\cos \left(2\right)$

$\mathrm{Tangent}\left(x^3-x\,-0.432\,\mathrm{view}=\left[-2..1\,\mathrm{DEFAULT}\right]\,\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{Tangent}\left(\tan \left(x\right)\,x=\frac{3}{2}\,\mathrm{output}=\mathrm{plot}\right)$

$\mathrm{Tangent}\left(x^2\,x=1\,\mathrm{output}=\mathrm{plot}\,\mathrm{showpoint}=\mathrm{false}\,\mathrm{tangentoptions}=\left[\mathrm{color}=\mathrm{green}\right]\right)$