Taylor Polynomials
The EPIC screen below shows the beginning of the choice for Taylor polynomials. The degree of the polynomial, and the x-coordinate of the expansion, frequently denoted by a in standard calculus textbooks, can be specified. If the option "Display Derivative Values" is set to Yes, then a table of the values of F(n)(a) are shown, for n = 0 ... Degree. And of course, "Draw graph" may be set to Yes or No to get the graph of the requested Taylor polynomial.
The next EPIC screen shows the graphs of 4 Taylor polynomials for F(x) = x cos(x), of degree 1, 3, 5, 7, along with the graph of F(x). These are labeled P1(x), P3(x), P5(x) and P7. The labeling was not done when the graphs were drawn. That process is "dynamic" - the screen changes as the new graph is drawn. The display here is "static", so the labels were added using the option "Write titles and labels" under the "Other" option available on the 2D Graphs main menu. Notice how the interval of agreement between F(x) and the Taylor polynomial expands as the degree increases - just what you want a student to realize!
