There are two ways to find a relative minimum value of a funtion, using GRAPH/TRACE and using GRAPH/MATH/FMIN. These procedures are illustrated below:
Find the relative minimum 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 minimum 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 the point on the
graph where it takes on the relative minimum 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. Do this a couple times.
Get back in trace mode with GRAPH/TRACE.
- use the left or right arrow keys to located the lowest point on the graph (we want the point whose y-coordinate is smaller than any around it.) You should have found that the point where the minimum value occurs is (.53518379667, -6.879419747), or perhaps you found a point close to this.
- Choose the GRAPH/MATH/FMIN 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 minimum point;
- one to the right of the relative minimum point; and
- a point close to the relative minimum 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 minimum point will be displayed at the bottom of the display. In this case you will get
Minimum
x = .53518379667 y = -6.879419747