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For `g(x)=e^x/(10x+3)` what is the minimum and maximum value for 0<x<5

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maheen100 | Student, Undergraduate | (Level 1) Honors

Posted January 22, 2013 at 11:45 PM via web

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For `g(x)=e^x/(10x+3)` what is the minimum and maximum value for 0<x<5

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted January 23, 2013 at 3:25 AM (Answer #1)

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The function `g(x) = (e^x)/(10x +3)` .

In the interval `x in (0, 5)`, the graph of the function is:

The maximum value lies at x = 5 and is equal to `(e^5)/(10*5 +3) ~~ 2.8`

The minimum value is estimated by solving `g'(x) = 0`

=> `(e^x*(10x+3) - e^x*10)/(10x+3)^2 = 0`

=> `e^x*(10x+3) - e^x*10 = 0`

=> `e^x*(10x+3) = e^x*10`

=> `10*x+3 = 10`

=> `x = 7/10`

=> `x = 0.7`

`g(0.7) ~~ 0.2013`

The minimum value of the function in the given interval for x is 0.2013 and the maximum value is 2.8

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