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Discuss the extremum of f(x)=1/3(x+1/x)...

Discuss the extremum of `f(x)=1/3(x+1/x)`

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Verified by Experts

The correct Answer is:
Point of local maxima :x=-1
Point of local minima:x=1
`f(x)=(1)/(3)(x+(1)/(x))`
`therefore f(x)=(1)/(3)(1-1)/(x^(2))`
`Let f(x) =0 or x^(2)=1 or x= pm 1` Also,
f''(x)=`(1/3)(2)/(x^(3)) or f''(1)gt0 and f''(-1)lt0`
Thus x =1 is point of minima and x=-1 is point of maxima
here f(1) =` (2/3) and f(-1)=(-2)/(3)`
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