Given a function (specified in the box labeled "$f(x)=$"), this demo plots $y=f(x)$ (in blue) and a dot at $(x,y)=(a,f(a))$ (according to the value of $a$ specified by the slider) as well as the line tangent to $y=f(x)$ at $x=a$ (a green dashed line). Derivative information and the equation of the tangent line are displayed below the plot.
If the "Show quadratic approximation?" box is checked, the quadratic approximation based at $x=a$ (i.e. second order Taylor polynomial) will also be computed and displayed (as a red dashed curve).
Several built in demos (with preset function, $a$ value, and plot domain) are provided in a drop down list. The limits of the slider bar are set using the plot domain. If you change a box entry, simply click outside the box to have sage recompute the plots and displayed values.
The computation above is powered by SageMath. The Sage code is embedded in this webpage's html file. To view the code instruct your browser to show you this page's source. For example, in Chrome, right-click and choose "View page source".