Pre-Calc Homework Solutions 187

Pre-Calc Homework Solutions 187 - Chapter 4 Review The...

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The second derivative is always positive (where defined), so the function is concave up for all x ± 0. Graphical support: [ 2 4, 4] by [ 2 1, 5] (a) [ 2 1, 0) and [1, ) (b) ( 2‘ , 2 1] and (0, 1] (c) ( 2‘ , 0) and (0, ) (d) None (e) Local (and absolute) minima at (1, e ) and ( 2 1, e ) (f) None 4. Note that the domain of the function is [ 2 2, 2]. y 95 x 1 } 2 ˇ 4 w 1 2 w x w 2 w } 2 ( 2 2 x ) 1 ( ˇ 4 w 2 w x w 2 w )(1) 5 } 2 x 2 ˇ 1 4 w ( 2 w 4 2 x w 2 w x 2 ) } 5 } ˇ 4 4 w 2 2 w 2 x x w 2 2 w } y 05 5 Note that the values x 56 ˇ 6 w are not zeros of y 0 because they fall outside of the domain. Graphical support: [ 2 2.35, 2.35] by [ 2 3.5, 3.5] (a) [ 2 ˇ 2 w , ˇ 2 w ] (b) [ 2 2, 2 ˇ 2 w ] and [ ˇ 2 w ,2] (c) ( 2 2, 0) (d) (0, 2) (e) Local maxima: ( 2 2, 0), ( ˇ 2 w ,2) Local minima: (2, 0), ( 2 ˇ 2 w , 2 2) Note that the extrema at x ˇ 2 w are also absolute extrema. (f) (0, 0) 5. y 1 2 2 x 2 4 x 3 Using grapher techniques, the zero of y 9 is x < 0.385. y 052 2 2 12 x 2 52 2(1 1 6 x 2 ) The second derivative is always negative so the function is concave down for all x . Graphical support: [ 2 4, 4] by [ 2 4, 2] (a) Approximately ( 2‘ , 0.385] (b) Approximately [0.385, ) (c) None (d) ( 2‘ , ) (e) Local (and absolute) maximum at < (0.385, 1.215)
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