As I stated in the intruction of my project for EMT 670 students in Korean high school are expected to solve complicated function problems without help of any technology. So the knowledge about differential calculus is as important as solving the problems themselves. Let us guess that a rational function is given.
Students can get a lot of information of the function with the differentiated function.
Students first will graph the simple figure of the function, and usually mark the roots of function, if possibly calculated, and some points where the differentiatial coefficients are zero. I think every knowledge from the process should be understood conceptually by students. I think the use of Algebra Xpressor will provide meaningful knowledge about questions raised above by comparing a mother function and its differentiated fuction visually in a scene. Next are an example of rational function . The graph can be easily drawn by Algebra Xprossor, but, the main focus is how to use it to make students understanding about relationship between a function and its differential function .