The function `f(x)=x^(3)-3x ` is

Options

A. increasing on `(-oo,-1) cup [1,oo)` and decresing on (-1,1)
B. decreasing on `(-oo,-1] cup [ 1,oo)` and increasing on (-1,1)
C. increasing on `(0,oo)` and decreaing on `(-oo,0)`
D. decreasin on `(0,oo) ` and increasing on `(-oo,0)`

Answer

A

Explanation

We have
`f(x)=x^3 -3x rArr f(x) =3x^2 -3`
For f(x) to be increasing we must have
`f(x) ge 0 rArr 3x^2-3 le 0 rArr x le -1 or x gt 1`
Hence f(x) increasing on `(-oo,-1] cup [ 1,oo)`and decreasing on (-1,1)