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If f(x)={(x^(alpha)logx , x > 0),(0, x=...

If `f(x)={(x^(alpha)logx , x > 0),(0, x=0):}` and Rolle's theorem is applicable to `f(x)` for `x in [0, 1]` then `alpha` may equal to (A) -2 (B) -1 (C) 0 (D) `1/2`

A

`-2`

B

`-1`

C

0

D

`(1)/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
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Knowledge Check

  • Let f (x)= [{:(x ^(2alpha+1)ln x ,,, x gt0),(0 ,,, x =0):} If f (x) satisfies rolle's theorem in interval [0,1], then alpha can be:

    A
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  • If f(x) = x^(a) log x and f(0) = 0 then the value of alpha for which Rolle's theorem can be applied in [0,1] is

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