If f(x)=x^(3)+ax^(2)+ax+x(tantheta+cott...

If `f(x)=x^(3)+ax^(2)+ax+x(tantheta+cottheta)` is increasing for all x and if `thetain(pi,(3pi)/(2))` then -

`a^(2)-3a-6lt0`

`a^(2)-3a-6gt0`

`a^(2)-3a-6le0`

`a^(2)-3a-6ge0`

Text Solution

Verified by Experts

The correct Answer is:

`f'(x)=3x^(2)+2ax +a +tantheta+cotthetage0`
`because tantheta+costhetage2AAthetain(pi,(3pi)/(2))`
`therefore 3x^(2) +2ax+a+2ge0`
D `le` 0
`rArra^(2)-3a-6le0`

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