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Pre-Calc Homework Solutions 146

# Pre-Calc Homework Solutions 146 - 146 Section 4.3 21...

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21. continued y 0 5 ( e 1/ x 2 )(4 x 2 3 ) 1 (1 2 2 x 2 2 )( e 1/ x 2 )( 2 2 x 2 3 ) 5 ( e 1/ x 2 )(2 x 2 3 1 4 x 2 5 ) 5 2 e 1/ x 2 1 } x 2 x 1 5 2 } 2 Graphical support: [ 2 12, 12] by [ 2 9, 9] (a) ( 2‘ , 2 ˇ 2 w ] and [ ˇ 2 w , ) (b) [ 2 ˇ 2 w , 0) and (0, ˇ 2 w ] (c) (0, ) (d) ( 2‘ , 0) (e) Local maximum: ( 2 ˇ 2 w , 2 ˇ 2 w e w ) < ( 2 1.41, 2 2.33); local minimum: ( ˇ 2 w , ˇ 2 w e w ) < (1.41, 2.33) (f) None 22. This problem can be solved using either graphical or analytic methods. For a graphical solution, use NDER to obtain the graphs shown. y y 9 y 0 [ 2 4.7, 4.7] by [ 2 3, 11] [ 2 4.7, 4.7] by [ 2 10, 10] [ 2 4.7, 4.7] by [ 2 10, 10] An analytic solution follows. y 9 5 x 2 } 2 ˇ 9 w 1 2 w x w 2 w } ( 2 2 x ) 1 ˇ 9 w 2 w x w 2 w (2 x ) 5 } 2 ˇ 3 x 9 w 3 2 w 1 x w 1 2 w 8 x } 5 } 2 ˇ 3 x 9 w ( x 2 w 2 2 x w 2 w 6) } y 0 5 5 5 6 x 4 2 81 x 2 1 162 }} (9 2 x 2 ) 3/2 (9 2 x 2 )( 2 9 x 2 1 18) 1 ( 2 3 x 3 1 18
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