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

Options

A. increasing in `(-oo,-1) uu (1,oo)` and decreasing in `(-1,1)`
B. increasing in `( 0,oo)` and decreasing in `(-,oo)`
C. decreasing in `(0,oo)` and increasing in `(-oo,0)`
D. decreasing in `(-oo,-1) uu (1,oo)` and increasing in `(-1,1)`

Answer

A

Explanation

We have, function `f(x) = x^(3) - 3x`
`implies f'(x) = 3x^(2) - 3 = 3(x + 1) (x - 1)`

Here, `f'(X) gt 0` in `(- oo, -1) uu (1, oo)` and `f(x) lt 0` in (-1,1)
`:. F(x)` is increasing in `(- oo, -1), uu (1,oo)` and decreasing in (-1,1)