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The function in which Rolle's theorem is...

The function in which Rolle's theorem is verified is:

A

`f(x)=log""((x^(2)+ab))/((a+b)x)` in [a, b] (where `0ltaltb`

B

`f(x)=(x-1)(2x-3)` in [1,3]

C

`f(x)=2+(x-1)^(2//3)` in [0,2]

D

`f(x)=cos""(1)/(x)` in [-1,1]

Text Solution

Verified by Experts

The correct Answer is:
A
(A)`f(x)=log(x^(2)+ab)-log(a+b)-logx`
f(x) is continuous in [a,b]
Now `f(x)=[(2x)/(x^(2)+ab)-(1)/(x)]` which clearly exists in `(a,b) and f(a)=f(b)=0`
So Rolle.s theorem is verfied.
(B) `f(1) ne f(3)`, So rolle.s theorem not satsified
(C) `f.(x)=(2)/(3(x-1)^(1//3))` Clearly f.(1) does not exist, so Rolle’s theorem is not satisfied.
(D) `f="cos"(1)/(x)` is Clearly does not exist, so Rolle’s theorem is not satisfied.
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