uc3rmw_0104e04

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.