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

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

A

Increasing `(-oo,-1) cup (1,oo)` and decreasing in `(-1,1)`

B

Decreasing `(-oo, -1) cup (1,oo)` and increasing in `(-1,1)`

C

Increasing `(0,oo)` and decreasing `(-oo,0)`

D

Decreasing in `(0,oo)` and increasing in `(-oo,0)`

Text Solution

Verified by Experts

The correct Answer is:
A
`f(x) = x^(3) - 3x`
`f.(x) = 3x^(2) - 3`
` = 3(x^(2) - 1)`
`f.(x) = 3 (x+1) (x-1)`
For increasing function
`f.(x) gt 0`
` x in (-oo, -1) uu(1,oo)`
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