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

Explanation

A function `f(x)` is increasing if `f^//x>0` and decreasing if `f^//x
`f(x)=x^3+1/x^3`

`f^//x=3x^2-3/(x^4)`

`impliesf^//x=frac(3x^6-3)(x^4)`

NOW ,

`f^//x>0,x∈(-1,0)and (1,infty)`

`f^//x<0,x∈(-infty,-1)and (0,1)`