Figure 3.7.2(a), an image of the  tutor, illustrates the features of the graph of $f\left(x\right)\=x^3\+5 x^2-17 x-9$ that can be determined from $f$ itself, and from the derivatives $f\prime$ and $f″$.

Where $f$ is increasing or decreasing, its graph is drawn in red or black, respectively,

Intervals where the graph of $f$ is concave up or down are shaded in gray or yellow, respectively.

Relative extrema and inflection points are shown in green.

Selecting one of the eight radio-buttons and clicking the "Calculate" button yields the information listed in Table 3.7.2(a).

Figure 3.7.2(b) uses the FunctionChart (a.k.a. FunctionPlot) command to draw the graph contained in Figure 3.7.2(a). The command provides slightly more control over the features of the graph. The symbols for the seven green points can be made larger, and arrows are used to indicate concavity.

The $x$-intercepts are marked with circles; the inflection points, with crosses; and the extreme points with diamonds. These distinctions are not visible in the tutor.

The point $\left[c_1\,f\left(c_1\right)\right]$ = $\left[-4.572599296\,77.67056587\right]$ is a relative maximum. The point   $\left[5\,f\left(5\right)\right]$ = $\left[5\,156\right]$ is also a relative maximum. From Figure 3.7.2(c), it is the absolute maximum.

The point $\left[c_2\,f\left(c_2\right)\right]$ = $\left[1.239265962\,-20.48538069\right]$  is a relative minimum. The point $\left[-9\,f\left(-9\right)\right]$ = $\left[-9\,-180\right]$ is also a relative minimum. From Figure 3.7.2(c), it is the absolute minimum.

From Figures 3.7.9 and 3.7.10, the function increases on the intervals $\left[-9\,c_1\right]$ = $\left[-9\,-4.572599296\right]$ and $\left[c_2\,5\right]$ = $\left[1.239265962\,5\right]$. The function decreases on the interval $\left[c_1\,c_2\right]$ = $\left[-4.572599296\,1.239265962\right]$.

From Figures 3.7.2(c) and 3.7.2(e), the function is concave upward on the interval $\left[p\,5\right]$ = $\left[-\frac{5}{3}\,5\right]$, and concave downward on the interval $\left[-9\,p\right]$ = $\left[-9\,-\frac{5}{3}\right]$  .

From Figures 3.7.2(c) and 3.7.2(e), the point $\left[p\,f\left(p\right)\right]$ = $\left[-\frac{5}{3}\,\frac{772}{27}\right]$$\doteq$$\left[-1.6667\,28.593\right]$   is an inflection point.

The endpoints of a finite domain for the function have to be considered when searching for extrema. If the domain is unrestricted, that is, if it is the full set of real numbers for which the rule of the function is defined, then for this function, there would not be a global maximum or minimum because $\left|f\left(x\right)\right|$ is unbounded as $x\to \pm \infty$.