A typical exercise in a Differential Calculus course is to obtain the equation of a line that is tangent to a function at a value of x. If you graph with different colors several lines that are tangent to a given function, at different values of x, then you obtain a "string art" image , it is also a good idea to let the students do all the calculation and graphing by hand besides using Mathematica , please notice there is also a great Demonstration of string art at string art Demonstration
Please find attached a Mathematica file with code for doing differential-calculus string-art
Have fun with Differential Calculus!
Jose from Mexico