Question: MA1210: Module 5 Polynomial and Rational Functions Discussion 5.1 Functions and Inequalities S. NO. 1. Problem () = 2 2 + 8 + 4 =

MA1210: Module 5 Polynomial and Rational Functions Discussion 5.1 Functions and Inequalities S. NO. 1. Problem () = 2 2 + 8 + 4 = b 8 = =4 2a 2(2) (4) = 2(4)2 + 8(4) + 4 (4) = 32 + 32 + 4 (4) = 4 Maximum at (4, 4) 2. () = 3 2 + 6 + 3 = b 6 = =1 2a 2(3) (1) = 3(1)2 + 6(1) + 3 (1) = 3 + 6 + 3 (1) = 12 Maximum at (1, 12) 3. () = 2 2 + 16 + 3 = b 16 = =4 2a 2(2) (4) = 2(4)2 + 16(4) + 3 (4) = 8 + 64 + 3 (4) = 59 Maximum at (4, 59) 4. () = 3 2 + 18 22 = b 18 = =3 2a 2(3) (3) = 3(3)2 + 18(3) 22 (3) = 27 + 56 22 (3) = 7 Maximum at (3, 7) 1 MA1210: Module 5 Polynomial and Rational Functions Discussion 5.1 Functions and Inequalities S. NO. 5. Problem () = 2 + 4 + 31 = b 4 = =2 2a 2(1) (2) = (2)2 + 4(2) + 31 (2) = 4 + 8 + 31 (2) = 43 Maximum at (2, 43) 6. () = 2 2 + 20 + 17 = b 20 = =5 2a 2(2) (5) = 2(5)2 + 20(5) + 17 (5) = 20 + 100 + 17 (5) = 97 Maximum at (5, 97) 7. () = 2 2 + 44 180 = b 44 = = 11 2a 2(2) (11) = 2(11)2 + 44(11) 180 (11) = 222 + 444 180 (11) = 42 Maximum at (11, 42) 8. () = 3 2 + 42 112 = b 42 = =7 2a 2(3) (7) = 3(7)2 + 42(7) 12 (7) = 147 + 294 12 (7) = 135 Maximum at (7, 135) 2 MA1210: Module 5 Polynomial and Rational Functions Discussion 5.1 Functions and Inequalities S. NO. 9. Problem () = 2 2 + 36 84 = b 36 = =9 2a 2(2) (9) = 2(9)2 + 36(9) 84 (9) = 162 + 333 84 (9) = 87 Maximum at (9, 87) 10. () = 2 + 16 50 = b 16 = =4 2a 2(2) (4) = (4)2 + 16(4) 50 (4) = 16 + 64 50 (4) = 2 Maximum at (4, 2) 11. () = 2 2 + 12 + 19 = b 12 = =3 2a 2(2) (3) = (3)2 + 12(3) + 19 (3) = 9 + 36 + 19 (3) = 346 Maximum at (3, 46) 12. () = 2 + 14 6 = b 14 = =7 2a 2(2) (7) = (7)2 + 14(7) 6 (7) = 49 + 98 6 (7) = 141 Maximum at (7, 141) 3 MA1210: Module 5 Polynomial and Rational Functions Discussion 5.1 Functions and Inequalities S. NO. 13. Problem () = 3 2 + 12 + 15 = b 12 = =4 (3) 2a (4) = 3(4)2 + 12(4) + 15 (4) = 48 + 48 + 15 (4) = 15 Maximum at (4, 15) 14. () = 2 + 20 40 = b 20 = = 10 2a 2(1) (10) = (10)2 + 20(10) 40 (10) = 20 + 200 40 (10) = 140 Maximum at (10, 140) 15. () = 2 2 + 28 52 = b 28 = =7 2a 2(2) (7) = 2(7)2 + 26(7) 52 (7) = 98 + 182 52 (7) = 32 Maximum at (7, 32) 16. () = 3 2 + 30 37 = b 30 = =5 2a 2(3) (5) = 3(5)2 + 30(5) 7 (5) = 75 + 150 7 (5) = 68 Maximum at (5, 68) 4 MA1210: Module 5 Polynomial and Rational Functions Discussion 5.1 Functions and Inequalities S. NO. 17. Problem () = 2 + 6 + 11 = b 6 = =6 (1) 2a (6) = (6)2 + 6(6) + 11 (6) = 36 + 36 + 11 (6) = 11 Maximum at (6, 11) 18. () = 3 2 + 24 29 = b 24 = =6 2a 2(3) (6) = 3(6)2 + 24(6) 29 (6) = 108 + 144 29 (6) = 7 Maximum at (6, 7) 19. () = 2 + 18 48 = b 18 = =9 2a 2(1) (9) = (9)2 + 18(9) 48 (9) = 81 + 153 48 (9) = 24 Maximum at (9, 24) 20. () = 2 2 + 4 + 54 = b 4 = =2 2a 2(2) (2) = 2(2)2 + 4(2) + 54 (2) = 8 + 8 + 54 (2) = 54 Maximum at (2, 54) 5 MA1210: Module 5 Polynomial and Rational Functions Discussion 5.1 Functions and Inequalities S. NO. 21. Problem () = 2 + 8 + 20 = b 8 = =4 2a 2(1) (4) = (4)2 + 8(4) + 20 (4) = 16 + 32 + 20 (4) = 34 Maximum at (4, 34) 22. () = 3 2 + 36 18 = b 36 = =9 2a 2(2) (9) = 3(9)2 + 36(9) 18 (9) = 243 + 324 18 (9) = 63 Maximum at (9, 63) 23. () = 2 + 24 82 = b 24 = = 12 2a 2(1) (12) = (12)2 + 24(12) 82 (12) = 144 + 288 82 (12) = 92 Maximum at (12, 62) 24. () = 3 2 + 48 153 = b 48 = =8 2a 2(3) (8) = 3(8)2 + 48(8) 153 (8) = 192 + 384 153 (8) = 423 Maximum at (8, 423) 6 MA1210: Module 5 Polynomial and Rational Functions Discussion 5.1 Functions and Inequalities S. NO. 25. Problem () = 2 + 12 + 24 = b 12 = =6 2a 2(1) (6) = (6)2 + 12(6) 24 (6) = 36 + 72 24 (6) = 12 Maximum at (6, 12) 26. () = 2 2 + 24 21 = b 24 = =6 2a 2(2) (6) = 2(6)2 + 24(6) 21 (6) = 24 + 144 21 (6) = 99 Maximum at (6, 99) 27. () = 2 2 + 32 83 = b 32 = =8 2a 2(2) (8) = 2(8)2 + 32(8) 83 (8) = 128 + 272 83 (8) = 61 Maximum at (8, 61) 28. () = 2 + 10 + 4 = b 10 = =5 2a 2(1) (5) = (5)2 + 10(5) + 4 (5) = 10 + 50 + 4 (5) = 44 Maximum at (5, 44) 7 MA1210: Module 5 Polynomial and Rational Functions Discussion 5.1 Functions and Inequalities S. NO. 29. Problem () = 2 + 28 154 = b 28 = = 14 2a 2(1) (14) = (14)2 + 28(14) 154 (14) = 194 + 392 154 (14) = 40 Maximum at (14, 40) 30. () = 2 + 2 + 15 = b 2 = =2 (1) 2a (2) = (2)2 + 2(2) + 15 (2) = 4 + 2 + 15 (2) = 23 Maximum at (2, 23) 8

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