what is the maxima and minima of x-(1/x)

plz ans with method thanks

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.

 

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)