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

Options

A. increasing in `(-oo,-1)cup(1,oo)` and decreasin in `(-1,1)`
B. increasing in `(0,oo)` and decreasingg in `(-oo,0)`
C. decreasing in `(0,oo)` and increasing in `(-oo,0)`
D. decreasing in `(-oo,-1)cup(1,oo)` and increasingg in (-1,1)

Answer

A

Explanation

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

here, `f'(x) ge 0 ` in `(-oo, -1)cup(1,oo) and f'(x) lt 0` in (-1,1) `thereforef(x)` is increasing `(-oo,-1),cup(1,00)` and decreasing in (-1,1).