SECTION 4.2 The Graph of a Polynomial Function; Models 211 Figure 24 22 0 250 30 Figure 22 22 0 250 30 Figure 25 Figure 23 ‘Are You Prepared?’ Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red. 4.2 Assess Your Understanding 1. What are the intercepts of y x5 10? = + (pp. 20–21) 2. Determine the leading term of x x 3 2 7 .3 + − (p. A23) 3. Use a graphing utility to approximate (rounded to two decimal places) any local maximum values and local minimum values of f x x x x 2 4 5, 3 2 ( ) = − − + for x 3 3. − ≤ ≤ (p. 93) 4. Use a graphing utility to find the quadratic function of best fit for the data below. (pp. 174–175) x 2 2.5 3 3.5 4 y 3.08 3.42 3.65 3.82 3.6 (a) Figure 22 shows the scatter plot. A cubic relation may exist between the two variables. (b) Upon executing the CUBIC REGression program on a TI-84 Plus CE, we obtain the results shown in Figure 23. The output shows the equation y ax bx cx d. 3 2 = + + + The cubic function of best fit to the data is C x x x x 0.0155 0.5951 9.1502 98.4327 3 2 ( ) = − + + (c) Figure 24 shows the graph of the cubic function of best fit on the scatter plot on a TI-84 Plus CE, and Figure 25 shows the result using Desmos. (d) Evaluate the function C x( ) at x 22. = C 22 0.0155 22 0.5951 22 9.1502 22 98.4327 176.8 3 2 ( ) = ⋅ − ⋅ + ⋅ + ≈ The model predicts that the cost of producing 22 thousand tumblers in a week will be 176.8 thousand dollars—that is, $176,800. Solution Now Work PROBLEM 43 Number of Tumblers, x (thousands) Cost, C ($1000s) 0 100 5 128.1 10 144 13 153.5 17 161.2 18 162.6 20 166.3 23 178.9 25 190.2 27 221.8 Table 6 Skill Building In Problems 5–22, analyze each polynomial function f by following Steps 1 through 8 on page 207. 5. f x x x 3 2 ( ) ( ) = − 6. f x x x 2 2 ( ) ( ) = + 7. f x x x 4 1 2 ( ) ( ) ( ) = + − 8. f x x x 1 3 2 ( ) ( )( ) = − + 9. f x x x 2 2 2 3 ( ) ( )( ) = − + − 10. f x x x 1 2 4 1 3 ( ) ( )( ) = − + − 11. f x x x x 1 2 4 ( ) ( )( )( ) = + − + 12. f x x x x 1 4 3 ( ) ( )( )( ) = − + − 13. f x x x x 1 2 ( ) ( )( ) = − − 14. f x x x x 3 2 1 ( ) ( )( )( ) = − + + 15. f x x x 1 2 2 2 ( ) ( ) ( ) = + − 16. f x x x 4 2 2 2 ( ) ( ) ( ) = − + 17. f x x x 2 1 16 2 2 ( ) ( ) ( ) = − − − 18. f x x x 3 1 9 2 2 ( ) ( ) ( ) = − + − 19. f x x x x 5 4 3 2 ( ) ( ) ( ) = − + 20. f x x x x 2 2 4 2 ( ) ( ) ( )( ) = − + + 21. f x x x x 2 3 2 2 ( ) ( ) ( ) = − + 22. f x x x x 1 4 2 2 ( ) ( ) ( ) = + + 1. Now Work 1. Modeling 1.ExplainingConcepts Calculus Preview 1.InteractiveFigure
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