The fourth degree function is given. It is easy for a high school students to differentiate the function. It will be . The next process is to find meaningful information from the two functions. When does the differentiated function have 0 as y-values? They are x=-1, x=1, and x=2 since y=12(x-2)(x+1)(x-1). It means that the graph of has points where the slopes of the tangent lines are 0. Let's see the table which explains the changes of values in detail.

y' means the changes of signs of slopes of tangent lines. Following is
the graph of . Even though the graph
does not have four distinct real roots since the graph intersect in two
different places on x-axis it is important for students to know the relationship
between the function and its differentiated
function .

The following graphs will explain about the relationship between the function and its differentiated function in detail.

The method of interpretation of a function and its differentiated function
is widely used in current Korean high school curriculum. In fact, students
are successful in drawing a graph with their calculation from a function
and its differentiated function just with pencil and paper. I hope that
providing them graphs from Algebra Xpressor will enhance their understanding
an important concept of calculus.