121616949-math.308 - -1< x< 0 or< x< 1 5.4.8...

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294 Appendix B Selected Answers 5.2.8. min at x = 7 π/ 12 + , max at x = - π/ 12 + , for integer k . 5.2.9. none 5.2.10. max at x = 0, min at x = ± 11 5.2.11. min at x = - 3 / 2, neither at x = 0 5.2.13. min at , max at π/ 2 + 5.2.14. min at 2 , max at (2 n + 1) π 5.2.15. min at π/ 2+2 , max at 3 π/ 2+2 5.3.1. min at x = 1 / 2 5.3.2. min at x = - 1, max at x = 1 5.3.3. max at x = 2, min at x = 4 5.3.4. min at x = ± 1, max at x = 0. 5.3.5. min at x = 1 5.3.6. none 5.3.7. none 5.3.8. min at x = 7 π/ 12 + , max at x = - π/ 12 + , for integer n . 5.3.9. max at x = 63 / 64 5.3.10. max at x = 7 5.3.11. max at - 5 - 1 / 4 , min at 5 - 1 / 4 5.3.12. none 5.3.13. max at - 1, min at 1 5.3.14. min at 2 - 1 / 3 5.3.15. none 5.3.16. min at 5.3.17. max at , min at π/ 2 + 5.3.18. max at π/ 2+2 , min at 3 π/ 2+2 5.4.1. concave up everywhere 5.4.2. concave up when x < 0, concave down when x > 0 5.4.3. concave down when x < 3, concave up when x > 3 5.4.4. concave up when x < - 1 / 3 or x > 1 / 3, concave down when - 1 / 3 < x < 1 / 3 5.4.5. concave up when x < 0 or x > 2 / 3, concave down when 0 < x < 2 / 3 5.4.6. concave up when x < 0, concave down when x > 0 5.4.7. concave up when x < - 1 or
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Unformatted text preview: -1 < x < 0 or < x < 1 5.4.8. concave down on ((8 n-1) π/ 4 , (8 n + 3) π/ 4), concave up on ((8 n + 3) π/ 4 , (8 n + 7) π/ 4), for integer n 5.4.9. concave down everywhere 5.4.10. concave up on (-∞ , (21-√ 497) / 4) and (21 + √ 497) / 4 , ∞ ) 5.4.11. concave up on (0 , ∞ ) 5.4.12. concave down on (2 nπ/ 3 , (2 n + 1) π/ 3) 5.4.13. concave up on (0 , ∞ ) 5.4.14. concave up on (-∞ ,-1) and (0 , ∞ ) 5.4.15. concave down everywhere 5.4.16. concave up everywhere 5.4.17. concave up on ( π/ 4+ nπ, 3 π/ 4+ nπ ) 5.4.18. inflection points at nπ , ± arcsin( p 2 / 3) + nπ 5.4.19. up/incr: (3 , ∞ ), up/decr: (-∞ , 0), (2 , 3), down/decr: (0 , 2) 6.1.1. max at (2 , 5), min at (0 , 1) 6.1.2. 25 × 25 6.1.3. P/ 4 × P/ 4 6.1.4. w = l = 2 · 5 2 / 3 , h = 5 2 / 3 , h/w = 1 / 2...
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