Students are given a function . I could find out an interesting feature from the graph with Algebra Xpressor. The function should have values no matter what the sign of x is. And, the function should have the same value for any two different x and -x. That means that the graph should be symmetric by y-axis.
Students can differentiate the function and they obtain .
The graph should pass through the origin. The following is the graph of by Algebra Xpressor, but it doesn't make sense at all according to our analysis. I thought that this could be a chanllenge for students to make a logical conjecture about the graph of the function and complete the half of it. The next is showing and . If students really understood the relationship between a function and its differential function, then this kind of limitation from the mathematical application itself would be easily corrected and make an advanced learning experience for the students.