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5.8 – Analyze Graphs of Polynomial Functions

This guide delves into the analysis of polynomial functions' graphs, focusing on turning points. Understand how to identify local maxima and minima through examples and explanations.

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5.8 – Analyze Graphs of Polynomial Functions

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  1. 5.8 – Analyze Graphs of Polynomial Functions

  2. 5.8 – Analyze Graphs of Polynomial Functions Example 1: Graph the function f(x) 1/6(x+3)(x – 2 )2

  3. 5.8 – Analyze Graphs of Polynomial Functions Example 2: Graph the function f(x)= 4(x+1)(x+2)(x – 1)

  4. 5.8 – Analyze Graphs of Polynomial Functions Example 3: Graph the function f(x)= 2(x+2)2(x+4)2

  5. 5.8 – Analyze Graphs of Polynomial Functions Turning Points Another important characteristic of graphs of polynomial functions is that they have turning points corresponding to local maximum and minimum values. The y-coordinate of a turning point is a local max of the function if the point is higher than all nearby points. The y-coordinate of a turning point is a local min of the function if the point is higher than all nearby points.

  6. 5.8 – Analyze Graphs of Polynomial Functions

  7. 5.8 – Analyze Graphs of Polynomial Functions Example 2: Graph the function f(x) = x3 – 3x2 + 6 Graph the function g(x)= x4 – 6x3+ 3x2 +10x – 3

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