# uc3rmw_0104e04

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In this example, we will
be using a graphing utility
to approximate the relative maximum
and the relative minimum point
on the graph of the function f of
x equals x cubed minus x squared.
The graph of f of x is shown.
By using the trace and
zoom features, we're going
to zoom in first on the relative maximum and
then use the trace feature to find out what
the relative maximum--
and we'll do the same thing
for the relative minimum.
So first, we'll zoom in
at the relative maximum.
The cursor is right at the
origin, where we see approximately
where the relative maximum is.
So we press Enter.
Now we press the Trace button
on the graphing calculator.
Now we can move left or right.
We see that the placement of that
trace point on the graph of f
is very close to what we see as the
relative maximum for this function,
and that point is at x, y equal to 0, 0.
Therefore, the relative maximum is
estimated to be 0 at x equals 0.
We're going to do the same thing
now for the relative minimum.
We'll zoom out a little bit
again, then zoom back in,
this time at the location
of the relative minimum,
and move the cursor over to the location
approximately of the relative minimum.
And go ahead and press Enter,
and the function gets re-graphed.
Now we go ahead and use
that trace feature again.
We find the placement of the
trace point on the graph of f
to be pretty close to the relative
minimum for this function.
We're going to move it over
to get a better estimate.
And it looks like we have a relative
minimum probably of around minus 0.15
at a value of x of 0.67.
Therefore, we see that there
is a relative minimum estimated
to be minus 0.15 at x equal 0.67.
So in summary, we see that
using the graphing utility,
we have a relative maximum at the point 0,
0 and a relative minimum at the point 0.67,
minus 0.15.