Pre-Calc Homework Solutions 189

Pre-Calc Homework Solutions 189 - Chapter 4 Review 10 This...

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10. This problem can be solved graphically by using NDER to obtain the graphs shown below. y y 9 y 0 [ 2 4, 4] by [ 2 1, 0.3] [ 2 4, 4] by [ 2 0.4, 0.6] [ 2 4, 4] by [ 2 0.7, 0.8] An alternative approach using a combination of algebraic and graphical techniques follows. Note that the denominator of y is always positive because it is equivalent to ( x 1 1) 2 1 2. y 95 5 y 05 5 5 } 2 ( x x 3 2 2 1 1 2 8 x x 1 2 3 1 ) 3 2 } Using graphing techniques, the zeros of 2 x 3 2 18 x 2 12 (and hence of y 0 ) are at x < 2 2.584, x < 2 0.706, and x < 3.290. (a) [ 2 ˇ 3 w , ˇ 3 w ] (b) ( 2‘ , 2 ˇ 3 w ] and [ ˇ 3 w , ) (c) Approximately ( 2 2.584, 2 0.706) and (3.290, ) (d) Approximately ( 2‘ , 2 2.584) and ( 2 0.706, 3.290) (e) Local maximum at 1 ˇ 3 w , } ˇ 3 w 4 2 1 } 2 < (1.732, 0.183); local minimum at 1 2 ˇ 3 w , } 2 ˇ 3 w 4 2 1 } 2 < ( 2 1.732, 2 0.683) (f) < ( 2 2.584, 2 0.573), ( 2 0.706, 2 0.338), and
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