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If f(x)=x^(5)-20x^(3)+240x, then f(x) sa...

If f(x)=`x^(5)-20x^(3)`+240x, then f(x) satisfies which of the following

A

It is decreasing everywhere

B

It is decreasing only in (0,`oo`)

C

It is increasing everywhere

D

It is incresing only in `(-oo,0)`

Text Solution

Verified by Experts

The correct Answer is:
3
`f'(x)=5x^(4)-60x^(2)=240`
`=5(x^(4)-12x^(2)+48)=5[(x^(2)-6)^(2)+12]`
`rArrf'(x)gt0AAinR`
i.e., f(x) is increasing everywhere
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