There are two ways to find a relative maximum value of a funtion, using GRAPH/TRACE and using GRAPH/MATH/FMAX. These procedures are illustrated below:
Find the relative maximum value of the polynomial funtion f(x) = x3 + 2x2 - 3x - 6
- Graph the function (see Graphing Functions);
The graph is shown below in the standard window. We will use GRAPH/TRACE to
find its relative maximum value and where that value occurs
- choose the TRACE option (F4) in the GRAPH menu;
- press the left or right arrow keys to move the trace cursor to a point on
the graph where it takes on the relative maximum value (indicated by the red
dot in the graph above.)
- to get a more accurate view of the graph around this point choose
GRAPH/ZOOM/ZIN and press ENTER. Do this at least once.
Get back in trace mode with GRAPH/TRACE.
- use the left or right arrow keys to located the highest point on the graph (we want the point whose y-coordinate is larger than any around it.) You should have found that the point where the maximum value occurs is (-1.868516961, .064660493193), or perhaps you found a point close to this.
- Choose the GRAPH/MATH/FMAX option (you will need to press the
MORE key to
display the MATH option in the GRAPH menu;
- This puts you in trace mode. You are being prompted to enter three
points:
- one to the left of the relative maximum point;
- one to the right of the relative maximum point; and
- a point close to the relative maximum point.
One way to do this is to use the left or right arrow keys to move the trace cursor to the left of the point and press ENTER. Now move the cursor to the right of the point and press enter. Finally, move the cursor as close as you can to the point and press enter. The coordinates of the relative maximum point will be displayed at the bottom of the display. In this case you will get
Maximum
x = -1.868516961 y = .064660493193