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f(x)=(logx)/(x)(xgt0) is increasing in...

`f(x)=(logx)/(x)(xgt0)` is increasing in

A

`(0,e)`

B

`(e,oo)`

C

`(0,oo)`

D

`(-oo,oo)`

Text Solution

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The correct Answer is:
A
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{:("List-I","List -II"),((A)f(x)=x^(2)-2x+5 "is increasing in","P"phi),((B)f(x)=e^(-x) "is increasing in ","q" (-oo,1)uu(2,oo)),((C)f(x)=logx "is increasing in","r" R),((D)f(x)=(x^(3))/(3)-(3x^(2))/(2)+2x+5 " is increasing in ","s"(0,oo)),(,t(1,oo)):}

Use the function f(x)=x^((1)/(x))(xgt0) to ascertain whether p^(e) or e^(p) is greater .

Obsereve the following the lists {:("List-I","List-II"),("A) "f(x)=x^2-2x+5" is increasing in","1) "xgt1/e),("B) "f(x)=x^x" decreases for","2) "(-oo,-1)uu(1,oo)),("C) "f(x)=x+1/x" is increasing in","3) "(1,oo)),("D) "f(x)=9-6x-2x^2-x^3" is decreasing for","4) "(-oo,oo)),("","5) "0ltxlt1/e):}