Find the intervals in which the function `f` given by `f(x)=\ x^3+1/(x^3)\ ,\ x\ !=0\ \ ` is (i) increasing (ii) decreasing.

Explanation

Given , ` f(x) = x^(3) + 1/x^(3)`
` rArr f'(x) = 3x^(2) - 3/x^(4)`
Let `f'(x) = 0 rArr 3x^(2) - 3/x^(4) =0 `
` rArr x^(6) - 1 = 0 " "(.:' x ne 0)`
` rArr (x-1)(x+1)(x^(4)0+x^(2)+1)=0`
` rArr x = 1 or x =- 1`
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(i) f(x) is increasing in `(-infty, -1]cup[1, infty)`.
(ii) f(x) is decreasing in `[-1, 1]-{0}`.