Pre-Calc Homework Solutions 137

Pre-Calc Homework Solutions 137 - Section 4.2 35. Possible...

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35. Possible answers: (a) (b) [ 2 2, 4] by [ 2 2, 4] [ 2 1, 4] by [0, 3.5] (c) [ 2 1, 4] by [0, 3.5] 36. Possible answers: (a) (b) [ 2 1, 5] by [ 2 2, 4] [ 2 1, 5] by [ 2 1, 8] (c) (d) [ 2 1, 5] by [ 2 1, 8] [ 2 1, 5] by [ 2 1, 8] 37. One possible answer: [ 2 3, 3] by [ 2 15, 15] 38. One possible answer: [ 2 3, 3] by [ 2 70, 70] 39. Because the trucker’s average speed was 79.5 mph, and by the Mean Value Theorem, the trucker must have been going that speed at least once during the trip. 40. Let f ( t ) denote the temperature indicated after t seconds. We assume that f 9 ( t ) is defined and continuous for 0 # t # 20. The average rate of change is 10.6 8 F/sec. Therefore, by the Mean Value Theorem, f 9 ( c ) 5 10.6 8 F/sec for some value of c in [0, 20]. Since the temperature was constant before t 5 0, we also know that f 9 (0) 5 0 8 F/min. But f 9 is continuous, so by the Intermediate Value Theorem, the rate of change f 9 (t) must have been 10.1 8 F/sec at some moment during the interval. 41.
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