The zeros and relative maximum and minimum points of a polynomial function may be found using a graphing calculator. One technique is to graph the function, choose the appropriate procedure from the math menu, and enclose the point in an interval by choosing a lower bound and an upper bound.
Example. Consider the function f (x) = x3 - 2x2 - 5x + 6. Find its zeros, relative maximum and relative minimum.
Solution: The graph is shown in the figure below. We see that there are three zeros. Obtain them one at a
time starting with the smallest. We give the method for the TI-92 Graphing Calculator. From the graph screen:
First zero: Select ‘Zero’: 
2 Lower bound: 
3 
Upper bound: 0 Zero: xc:
- 2 yc: 0
Second zero: Select ‘Zero’:
2 Lower bound: 0 Upper
bound: 2 Zero: xc: 1 yc:
0
Third zero: Select ‘Zero’:
2 Lower bound: 2 Upper
bound: 4 Zero: xc: 3 yc:
0
The zeros are - 2, 1, 3.
Relative maximum: Select ‘Maximum’:
4 Lower bound: 2
Upper bound: 0 Maximum:
xc: - .7863 yc: 8.20882
Relative minimum: Select ‘Minimum’:
3 Lower bound: 0 Upper
bound: 3 Minimum: xc:
2.11963 yc: - 4.06067
Problem. Consider the function f (x) = x3
- 2x2 -
5x + 6. Find its zeros, relative maximum and relative minimum.
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