Exercises Chapter 4 - 4.1 Extreme Values of Functions 243...

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Unformatted text preview: 4.1, Extreme Values of Functions 243 ES 4.1 l-6. determine from the graph whether the function has €xtreme values on fa, b]. Then explain how your answer n"rth Theorem l. cr c2 } : g(r) \.--10. find the extreme values and where thev occur. /- .8. 1' InE 11. xercises ll-14, match the table with a graph. 12. I',@) l'(x) 13. a0 b0 c-5 a0 b0 c5 CI b c a b c 14. l'(x) I',@) does not exist-2 does not exist does not exist-1.7 I I abc (d) In Exercises l5-34, find the absolute maximum and minimum values of each function on the given interval. Then graph the function. Iden- tiff the points on the graph where the absolute extrema occur, and in- clude their coordinates. ) lS.f(x):|x-5, -2<x<3 5 16.f(x):-x-4, -4<x<l 17.f(x):x2-I, -l<x<2 1S./(x):4-x2, -3<x<1 1 19. F(x):--j-, 0.5 3x<2 ,, 20. F(x\:-:, -2 <x< -l 21. h(x) : t[, -1 <.r = 8 22. h(x) - -3x2/3, -1 < x < | 23.g(x):f4-*2, -2<xsl I t I I c I a (a) I I I i a C (b) I I I a I I C b (c) 244 Chapter 4: AppLications of Derivatives 2a. sG) : -fi - x2, -ft < x s o 25. l(0): sing, -+ ' 0 - 4 2-"- 6 26. frcl: tan g, -t = u = T 27.g(.r):csc-r, T=*=+ 55 28. g(x): secx. -: = , = T 29. f(t) :2 - ltl, -l < t < 3 30. f(t): lr-51, 4<t<7 3l.g(x):x€', -l<x<l 32. h(x): ln(x * l), 0 = -r < 3 I 33. /(x) :' * lnx, 0.5 < x < 4 34.g(x):€', -2<x<l In Exercises 35-38, find the function's absolute maximum and mini- mum values and say where they are assumed. 35. /(x) : x413, -l < x < 8 36. f(x): x513, -1 < x < 8 37.5@):0315, -32<0<l 35. h(0):302/3, -27 < 0 < 8 In Exercises 39-54, find the extreme values of the function and where they occur. 39. Y:2x2 - 8x * 9 4l.Y:x3+x2-Bx+5 43.y:f;2-l 45. v " t/t-x2 47. v - -J- ' x"l7 49.Y:e'+e' 51. y:xlnx 53. y : cos-'("') y:x3-2x-1 4 y:x3-3x2*3x-2 I .Y- / ^ Yl - x' y:\,5+z*-^s x*l v-- xz*2x1-2 Y: et - e-x !: x2lnx , -t -- l, : sln '(e^) ( t , I 15 l-Zx'-tx* 4, x< 62.y:\'t |.r'-6x2+8x, x)r In Exercises 63 and 64, give reasons for your answers. 63. Let f(r) : (x - 212/z . a. Does /'(2) exist? b. Show that the only local extreme value of / occurs at x : 2. c. Does the result in part (b) contradict the Extreme Value Theorem? d. Repeat parts (a) and (b) for /(x) : (x - o)213 ,replacing 2by a. 64. Let f(r) : lx3 - 9xl . a. Does /'(0) exist? b. Does /'(3) exist? c. Does f'(-3) exist? d. Determine all extrema of /. 65. A minimum with no derivative The function f(x): lxl has an absolute minimum value at x : 0 even though / is not differ- entiable at x : 0. Is this consistent with Theorem 2? Give rea- sons for your answer. 66. Even functions If an even function /(x) has a local maximum value at x : c, can anything be said about the value of / at x : -c? Give reasons for your answer. 67. Odd functions If an odd function g(x) has a local minimum value at x : C, can anything be said about the value of g at x : *c?...
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This note was uploaded on 05/08/2011 for the course ACCOUNTING 121210 taught by Professor Sdasdas during the Spring '10 term at Albany College of Pharmacy and Health Sciences.

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Exercises Chapter 4 - 4.1 Extreme Values of Functions 243...

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