Chap6 Section3

Elementary and Intermediate Algebra: Graphs & Models (3rd Edition)

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Section 6.3 Extrema and Models 593 Version: Fall 2007 6.3 Exercises In Exercises 1 - 8 , perform each of the following tasks for the given polynomial. i. Without the aid of a calculator, use an algebraic technique to identify the zeros of the given polynomial. Factor if necessary. ii. On graph paper, set up a coordinate system. Label each axis, but scale only the x -axis. Use the zeros and the end-behavior to draw a “rough graph” of the given polynomial with- out the aid of a calculator. iii. Classify each local extrema as a rela- tive minimum or relative maximum . Note: It is not necessary to find the coordinates of the relative extrema. Indeed, this would be difficult with- out a calculator. All that is required is that you label each extrema as a relative maximum or minimum. 1. p ( x ) = ( x + 6)( x 1)( x 5) 2. p ( x ) = ( x + 2)( x 4)( x 7) 3. p ( x ) = x 3 6 x 2 4 x + 24 4. p ( x ) = x 3 + x 2 36 x 36 5. p ( x ) = 2 x 3 + 5 x 2 42 x 6. p ( x ) = 2 x 3 3 x 2 44 x 7. p ( x ) = 2 x 3 + 4 x 2 + 70 x 8. p ( x ) = 6 x 3 21 x 2 + 90 x In Exercises 9 - 16 , perform each of the following tasks for the given polynomial. i. Use a graphing calculator to draw the Copyrighted material. See: 1 graph of the polynomial. Adjust the viewing window so that the extrema or “turning points” of the polynomial are visible in the viewing window. Copy the resulting image onto your home- work paper. Label and scale each axis with xmin, xmax, ymin, and ymax. ii. Use the maximum and/or minimum util- ity in your calculator’s CALC menu to find the coordinates of the extrema. Label each extremum on your home- work copy with its coordinates and state whether the extremum is a rel- ative or absolute maximum or mini- mum. 9. p ( x ) = x 3 8 x 2 5 x + 84 10. p ( x ) = x 3 + 3 x 2 33 x 35 11. p ( x ) = x 3 + 21 x 20 12. p ( x ) = x 3 + 5 x 2 + 12 x 36 13. p ( x ) = x 4 50 x 2 + 49 14. p ( x ) = x 4 29 x 2 + 100 15. p ( x ) = x 4 2 x 3 39 x 2 + 72 x + 108 16. p ( x ) = x 4 3 x 3
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