Mth141S35n - Sec 3.5 Higher Degree Polynomial Functions and...

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Sec. 3.5 – Higher Degree Polynomial Functions and Graphs In the first chapter we discussed linear functions, ( 29 f x mx b = + , and earlier in chapter 3, we discussed quadratic functions, 2 ( ) f x ax bx c = + + . Now we are going to consider polynomial functions in general. Definition : A polynomial function P(x) is given by 1 2 2 1 2 2 1 0 ( ) ... n n n n n n P x a x a x a x a x a x a - - - - = + + + + + + where the coefficients ? a are real numbers and the exponents are whole numbers. Note that the constant function ( ) f x c = , a linear function ( ) f x mx b = + , and a quadratic function 2 ( ) f x ax bx c = + + are special cases of a polynomial function. A third degree polynomial function is called a cubic function. Ex. 3 2 ( ) 2 3 5 f x x x x = - + - A fourth degree polynomial function is called a quartic function. Ex. 4 3 2 ( ) 3 3 1 f x x x x x = - + + - We previously saw special properties of degree 0, 1, and 2 polynomial functions and their graphs. ??? These points are the “high” and “low” points of the function. An absolute maximum/minimum value is the y-coordinate of the highest/lowest point on the entire graph. A local maximum/minimum value is the y-coordinate of the highest/lowest point on a specified interval of the graph (also sometimes called the relative maximum/minimum.). A local maximum/minimum point is not necessarily the highest and lowest points on the function. They are points where the graph changes direction. See some examples.
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This note was uploaded on 06/06/2011 for the course MTH mth141 taught by Professor Stean during the Spring '10 term at Moraine Valley Community College.

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Mth141S35n - Sec 3.5 Higher Degree Polynomial Functions and...

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