1. 6.5/6.8 Analyze Graphs of Polynomial Functions
Relative Maximum and Minimum:
the y-coordinate values at each turning point in the graph of a polynomial.
*These are the highest and lowest points in the near by area of the graph
At most each polynomial has one less turning point than the degree

2. Graph:
f(x) = x4 - 13x2 + 36

3. Graph:
g(x) = 6x3 + 5x2 – 9x + 2

4. Graph:
f(x) = x4 – x3 – x2 – x – 2

5. Descartes’ Rule: used to determine how many positive real zeros, negative real zeros and imaginary zeros a polynomial has
Total number of zeros = degree
In f(x) the number of sign changes is the same as number of positive real zeros (or less by a multiple of 2)
In f(-x) the number of sign changes is the same as the number of negative real zeros (or less by a multiple of 2)
Imaginary zeros are based on how many possible real zeros compared to the total number of zeros

6. Use Descartes’ rule to determine how many of each type of zero is possible.
Ex 1. f(x) = x3 – x2 – 4x + 4

7. Find the location of all possible real zeros
Find the location of all possible real zeros. Then name the relative minima and maxima as well as where they occur
Ex 2. f(x) = x4 – 7x2 + x + 5