Pre-Calc Homework Solutions 139

Pre-Calc Homework Solutions 139 - Section 4.3 139...

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Exploration 2 Finding f from f 9 and f 0 1. f has an absolute maximum at x 5 0 and an absolute minimum of 1 at x 5 4. We are not given enough information to determine f (0). 2. f has a point of inflection at x 5 2. 3. [ 2 3, 5] by [ 2 5, 20] Quick Review 4.3 1. x 2 2 9 , 0 ( x 1 3)( x 2 3) , 0 Solution set: ( 2 3, 3) 2. x 3 2 4 x . 0 x ( x 1 2)( x 2 2) . 0 Solution set: ( 2 2, 0) < (2, ) 3. f: all reals f 9 : all reals, since f 9 ( x ) 5 xe x 1 e x 4. f: all reals f 9 :x ± 0, since f 9 ( x ) 5 } 3 5 } x 2 2/5 5. f: x ± 2 f 9 ± 2, since f 9 ( x ) 5 } ( x 2 2 ( x )( 2 1) 2 2 ) 2 ( x )(1) }5 } ( x 2 2 2 2) 2 } 6. f: all reals f 9 ± 0, since f 9 ( x ) 5 } 2 5 } x 2 3/5 7. Left end behavior model: 0 Right end behavior model: 2 x 2 e x Horizontal asymptote: y 5 0 8. Left end behavior model: x 2 e 2 x Right end behavior model: 0 Horizontal asymptote: y 5 0 9. Left end behavior model: 0 Right end behavior model: 200 Horizontal asymptotes: y 5 0, y 5 200 10. Left end behavior model: 0 Right end behavior model: 375 Horizontal asymptotes: y 5 0, y 5 375 Section 4.3 Exercises 1. (a) Zero: x 56 1; positive: ( 2‘ , 2 1) and (1, ); negative: ( 2 1, 1) (b) Zero: x 5 0; positive: (0, ); negative: ( 2‘ ,0) 2. (a) Zero: x < 0, 6 1.25; positive: ( 2 1.25, 0) and (1.25, ); negative: ( 2‘ , 2 1.25) and (0, 1.25) (b) Zero: x < 6 0.7; positive: ( 2‘ , 2 0.7) and (0.7, ); negative: ( 2 0.7, 0.7) 3. (a) ( 2‘ , 2 2] and [0, 2] (b) [ 2 2, 0] and [2, ) (c) Local maxima:
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