so ar Does the function in Example 6 have minimum at x = 2, a an absolute minimum on the interval (-0, +00) ? (See page 164 for answers., QUICK CHECK EXERCISES 3.4 to determine the absolute maximum and absolute minis values, if any, for f on the indicated intervals. 1. Use the accompanying graph to find the x-coordinates of (a) [1, 4] (b) [- 2, 2] (c) [-4, 4] the relative extrema and absolute extrema of f on [0, 6]. ( d) 14 -3 -2 - 1 0 -4 2 3 (x) 2224 -1333 0 1603 2096 2293 2400 2717 61 y = f(x) NW A 3. Let f(x) =x3 - 3x2 -9x + 25. Use the derivative f'() 3(x + 1)(x -3) to determine the absolute maximum absolute minimum values, if any, for f on each of the g Figure Ex-1 intervals. (a) [0, 4] (b) [ - 2, 4 ] (c) [-4, 2] 2. Suppose that a function f is continuous on [-4, 4] and has (d) [-5, 10] (e) (-5, 4) the behty critical points at x = -3, 0, 2. Use the accompanying table EXERCISE SET 3.4 Graphing Utility C CAS FOCUS ON CONCEPTS (c) f has relative minima at x = 1 and x = 8, has rel. 1-2 Use the graph to find x-coordinates of the relative ex- ative maxima at x = 3 and x = 7, has an absolute trema and absolute extrema of f on [0, 7]. minimum at x = 5, and has an absolute maximum a x = 10. 4. In each part, sketch the graph of a continuous functionj with the stated properties on the interval (-co, too). (a) f has no relative extrema or absolute extrema. (b) f has an absolute minimum at x = 0 but no absolute maximum. (c) f has an absolute maximum at x = -5 and an abso- 3. In each part, sketch the graph of a continuous function f lute minimum at x = 5. with the stated properties on the interval [0, 10]. 5. Let (a) f has an absolute minimum at x = 0 and an absolute maximum at x = 10. (b) f has an absolute minimum at x = 2 and an absolute maximum at x = 7. f ( x) = 0