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If f(x)=x+1/x ,\ \ x >0 , then its great...

If `f(x)=x+1/x ,\ \ x >0` , then its greatest value is `-2` (b) 0 (c) 3 (d) none of these

A

`-2`

B

`0`

C

`3`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
D
Given, `f(x)=x+(1)/(x)`
On differentiating w.r.t. x, we get
`f'(x)=1-(1)/(x)`
and `f"(x)=(2)/(x^(3))`
Put `f'(x)=0` for maxima or minima
`thereforex^(2)-1=0`
`impliesx=+-1`
At `x=-1,f"(x)lt0`
`impliesf(x)` is maxima.
but xgt0.
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