Let S be the set of real values of param...

Let S be the set of real values of parameter `lamda` for which the equation f(x) = `2x^(3)-3(2+lamda)x^(2)+12lamda` x has exactly one local maximum and exactly one local minimum. Then S is a subset of

A

`(4,oo)`

B

`(-3, 3)`

C

`(3, oo)`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:

B

`f(x)=2x^(3)-3(2+lamda)x^(2)+12lamdax`
`rArr f'(x)= 6x^(2)-6(2+lamda)x+12lamda`
`f'(x)= 0 rArrx=2,lamda`
If `f(x)` has exactly one local maximum and exactly one local minimum, then `lamdane2`.

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