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

A function f(x) is increasing if `f′(x)>0` and decreasing if `f′(x)<0`

`f(x)=\ x^3+1/(x^3)`

`​f′(x)=3x^2−3/x^4​=(3x^6−3​)/x^4`

Now,

`f′(x)>0 ,x∈(−1,0) `and `(1,∞)`

`f′(x)<0,x∈(−∞,−1)` and `x∈(0,1)`