3.4 Absolute Extrema 2 16. f{x) = E (a) [7,12] (b) [-3,2] (c) [4,9] For Exercises 17 - 21, find the absolute maximum and minimum of f on each of the given intervals, if they exist. 17. f(x)=x" +15% +27x~1 (@) (-11,0) (b) [-14,2) (c) (-4,3] 18. f(x)=x" =5x* =202 + 100 (a) (-1,8] (b) (-3,7) (c) [-4,-1) 19. f(x) =3x* 44x - 360x + 50 (a) [-6,0) (b) (12,18] (c) (-1,20) 20. f(x)= # (a) [-9,5] (b) [-3,6] (c) [-1.6] Il 21 f(0)= (@) [-5,-1] (b) [-8.4] (c) [-6,0] 3.4 Absolute Extrema For Exercises 25 and 26, the graph of f is shown. Find the absolute extrema of f on each of the given intervals, if they exist. (@) (-8,-4) (b) [0.6) (c) [1.3] (@) [-3.2] () (-1.5) () [2,8) For Exercises 27 - 34, find the absolute maximum and minimum of f on each of the given intervals. 27. f(x)=(x=2)e* (a) [0,2] (b) [-5,0] () [1,3] 28, f()=(2-4) Chapter 3: Curve Sketching & Optimization (a) [-4,-1] (b) [-1,3] (c) [-5,5] 29. f(x) = In(x) (a) [1,3] (b) [1/2, Vel find the absolute (c) [2,4] maximum and 30. f(x) = (+2 -1)2 (a) [-2,3] minimum of f on each (b) [-1,4] (c) [-1, 1] of the given intervals 31. f(x) = e-x (a) [-7,-3] (b) [-1, 1] (c) [0,3/2] 32. f(x) = 4x2 In(x) (a) [1,3] (b) [2,5] (c) [1/10,3/4] 33. f(x) = 2 -9 (a) [-15,-10] (b) [-2, 1] (c) [4,6] 34. f(x) = x-51n(x) (a) [1,6] (b) [2,4] (c) [15,20]3.4 Absolute Extrema For Exercises 35 - 40, find the absolute maximum and minimum of f on each of the given intervals, if they exist. A 2-4x+4 (a) [1,6] (b) [-8,0) () (-2,4] 35 f(x)= 36. f(0) = /(2 -3x)" @ [-4,1) b) (2,5) (c) (0,3] i 2+4 (a) (-8,4) (b) (-2,2] (c) [0,6) 37. f(x)= -5e* 2 (a) (-1,3) (b) (1,4] (c) (5,8] 38. f(x)= 39. f(x) = In(x)-2x* (a) [1/3,8/9) (b) (1/2,4) (c) (0,2] 241 NS0 = 52 (a) [-4,3) (b) [-7.2] (c) (1,7]