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

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

Graph: g(x) = 6x3 + 5x2 – 9x + 2

Graph: f(x) = x4 – x3 – x2 – x – 2

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

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

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