Answers of Exercise 4.1 on Calculus and Its Applications | MS 120, Assignments of Mathematics

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Answers A-27 CHAPTER 4 Exercise 4-1 L@bs (AeA) 3 Beslads(fe) Radf Taf 9. Local maximum at x = @; local minimum at x = ¢;no |} extrema atx = band x = d 11. Decreasing on (—oe, 4); increasing on (4, 00); local minimum at x = 4 13, Incteasing on (oo, —4); decreasing on (—4, 00); local maximum atx = —4 45, Increasing for all x: no local extrema 17. Decreasing on (~o0, 0) and (6, 00); inereasing on (0, 6); local minimum at x = 0: Jocal maximum atx — 19. Tncreasing on (~00, —2) and (3, co); decreasing on (~2, 3); local maximum at x = —2, local minimum at x = 3 21, Decreasing on. (~o0, 3) and (8, 3); increasing on (3, 0) and (3, oc); local minima at x = —3 and x = 3 local maximum atx =0 23, Increasing on (—ve, 2); decreasing on (2, 00); lacal maximum at x = 2 25, Decreasing on (—po, ~ increasing on (—0.39, co); local minimum at x = —0.39 27. Decreasing on (—oo, 0.77) and (1,08, 2.69); increasing on (-0.77, 1.08) and (2.69, 00); local minima at x = 0.77 and * = 2.69; local maximum ai x = 1.08 29, Decreasing on (—o0, ~1,22) and (0.35, 2.38); increasing on (1.22, 0.35) and (2.38, oc); local minima at x = ~1.22 and x = 2.38; local maximum at x = 0.35 31. Increasing on (—cx, 4) 33. Increasing on (-co,~1), (1,00) 35, Decreasing for all x Decreasing on (4, 00) Decreasing on (-1, 1) Horizontal tangent at x = 2 Horizontal tangent at x = 4 Horizontal tangents at x = —1,1 Fox) fo fe) Bog, Ags WD. gy 51, Increasing on.(—1, 2); decreasing on (—oo, ~1) and (2,00); $3. Tnereasing on (1, 2) and (2, 00): decreasing on local minimum at x = —1; local maximum atx = 2 (-00,-1); local minimum atx = —1 fa) fa 55. Increasing on (--2, 0) and (3, 00); decreasing on (—co, -2) and (0, 3); local minima at x = —2 and x°= 3: loval maximum atx=0 fo