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If f(x)=x^(3/2)(3x-10),xgeq0, then f(x) ...

If `f(x)=x^(3/2)(3x-10),xgeq0,` then `f(x)` is increasing in ____.

A

`(-oo ,-1)cup(1,oo)`

B

`[2,oo)`

C

`(-oo,-1 ) cup [1,oo)`

D

`(-oo,0] cup (2,oo)`

Text Solution

Verified by Experts

The correct Answer is:
B
We hve `f(x)=x^(3/2)(3x-10),x ge 0`
`rArr f(x)=3/2x^(1//2)(3x-10)+x^(3//2) xx 3= 15/2x^(1//2) (x-2)`
For f(x) to be increasing we must have
`f(x) ge 0 rArr 15/2 x^(1/2/)(x-2) ge 0 rArr x le 2 rArr x in [2,oo)`
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