Pre-Calc Homework Solutions 144

Pre-Calc Homework Solutions 144 - 144 Section 4.3 17....

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17. continued (a) ( 2‘ , ) (b) None (c) ( 2‘ , 5 ln 3) < ( 2‘ , 5.49) (d) (5 ln 3, ) < (5.49, ) (e) None (f) 1 5 ln 3, } 5 2 } 2 < (5.49, 2.50) 18. 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 6, 10] by [0, 4] [ 2 6, 10] by [0, 0.6] [ 2 6, 10] by [ 2 0.15, 0.15] An analytic solution follows. y 5 } 2 e 2 x 8 1 e 2 5 x e 2 1.5 x }5 } 2 1 5 8 e 2 0.5 x } y 95 5 } (2 1 20 5 e e 2 2 0. 0 5 . x 5 x ) 2 } Since y 9. 0 for all x , y is increasing for all x . y 05 5 5 Solve y 0: 5 e 2 0.5 x 2 2 5 0 e 2 0.5 x 5 } 2 5 } 2 0.5 x 5 ln } 2 5 } x 52 2 ln } 2 5 } 5 2 ln } 5 2 } (a) ( 2‘ , ) (b) None (c) 1 2‘ , 2 ln } 5 2 } 2 < ( 2‘ , 1.83) (d) 1 2 ln } 5 2 } , 2 < (1.83, ) (e) None (f) 1 2 ln } 5 2 } ,2 2 < (1.83, 2) 10 e 2 0.5 x (5 e 2
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