Pre-Calc Homework Solutions 140

Pre-Calc Homework Solutions 140 - 140 8. y Section 4.3 6x 2...

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8. y 952 6 x 2 1 12 x 52 6 x ( x 2 2) y 052 12 x 1 12 12( x 2 1) Graphical support: [ 2 4, 4] by [ 2 6, 6] (a) [0, 2] (b) ( 2‘ , 0] and [2, ) (c) ( 2‘ ,1) (d) (1, ) (e) Local maximum: (2, 5); local minimum: (0, 2 3) (f) At (1, 1) 9. y 95 8 x 3 2 8 x 5 8 x ( x 2 1)( x 1 1) y 05 24 x 2 2 8 5 8( ˇ 3 w x 2 1)( ˇ 3 w x 1 1) Graphical support: [ 2 4, 4] by [ 2 3, 3] (a) [ 2 1, 0] and [1, ) (b) ( 2‘ , 2 1] and [0, 1] (c) 1 2‘ , 2} ˇ 1 3 w } 2 and 1 } ˇ 1 3 w } , 2 (d) 1 2} ˇ 1 3 w } , } ˇ 1 3 w } 2 (e) Local maximum: (0, 1); local (and absolute) minima: ( 2 1, 2 1) and (1, 2 1) (f) 1 6} ˇ 1 3 w } , 2} 1 9 } 2 10. y xe 1/ x ( 2 x 2 2 ) 1 e 1/ x 5 e 1/ x 1 1 2 } 1 x } 2 y e 1/ x ( x 2 2 ) 1 1 1 2 } 1 x } 2 e 1/ x ( 2 x 2 2 ) 5 } e x 1 3 / x } Graphical support: [ 2 8, 8] by [ 2 6, 6] (a) ( 2‘ , 0) and [1, ) (b) (0, 1] (c) (0, ) (d) ( 2‘ ,0) (e) Local minimum: (1, e ) (f) None 11. y x } 2 ˇ 8 w 1 2 w x w 2 w } ( 2 2 x ) 1 ( ˇ 8 w 2 w x w 2 w )(1) 5 } ˇ 8 8 w 2 2 w 2 x x w 2 2 w } y 5 } ( 2 8 x 2 3 2 x 2 2 ) 4 3/ x 2 }5 } 2 ( x 8 ( x 2 2 2 x 2 ) 1 3 2 /2 ) } Graphical support: [ 2 3.02, 3.02] by [ 2 6.5, 6.5] (a) [ 2 2, 2] (b) [ 2 ˇ 8 w , 2 2] and [2, ˇ 8 w ] (c) ( 2 ˇ 8 w (d) (0, ˇ 8 w ) (e) Local maxima: ( 2 ˇ 8 w , 0) and (2, 4); local minima: ( 2 2, 2 4) and ( ˇ 8 w Note that the local extrema at x 56 2 are also absolute extrema. (f) (0, 0) ( ˇ 8 w 2 w x w 2 w )( 2 4 x ) 2 (8 2 2 x 2 ) } 2 ˇ 8 w 1 2 w x w 2 w } ( 2 2 x ) }}}}} ( ˇ 8 w 2 w x w 2 w ) 2 140 Section 4.3 Intervals x , 1 x . 1 Sign of y 01 2 Behavior of y Concave up Concave down Intervals x , 00 , x , 11 , x Sign of y 91 2 1 Behavior of
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This note was uploaded on 10/05/2011 for the course MAC 1147 taught by Professor German during the Fall '08 term at University of Florida.

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