Find the interval(s) over which the function is increasing and/or decreasing.
First, find the derivative of the function as follows:
Suppose is a differentiable function over the interval . If
for all , then is an increasing function of over the interval .
Likewise, if for all , then is a decreasing function of
over the interval . For this reason, the function is increasing
when , and it is decreasing when . Now, to help determine the
values of that satisfy the inequalities and , solve the
This means that the zeros of the function are and . Next, graph the function .
The graph shows that the values of that satisfy the inequality
are and , and the values
of that satisfy the inequality are . Thus, the function is
increasing over the intervals and , and it is decreasing over
the interval .