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what is the maxima and minima of x-(1/x) plz ans with method thanks

what is the maxima and minima of x-(1/x)
plz ans with method thanks

Grade:12

2 Answers

Vikas TU
14149 Points
4 years ago
Differentiate it:
f(x) = x – 1/x (given)
df/dx = 1 + 1/x^2 > 0
Hence it is an increasing function.
The function grapgh will always increase monotonically.
with slope positive.
And it will cut x- axis at 1 ass it satiffiess it.and it will never touch y- axis as x cannot be equal to zero.
 
Further at x infinity y is infinity
and at x – infinithy y is – infinity.
 
maxima is + infinity 
and minima = – infinity.
 
swapnil
16 Points
4 years ago
let Y=x-1/x                                                                                                                                                                                                                       upon differentiating we get dy/dx=1+1/x^2                                                                                                                                                                         hence dy/dx always positive then it will always increses monotonically                                                                                                                                 then at x=infinity y=infinity(maxima) and x=-infinity y=-infinity(minima)                                                                                                                                  hence range of function will be (-infinity,infinity)

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