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Statement 1: If g(x) is a differentiable...

Statement 1: If `g(x)` is a differentiable function, `g(2)!=0,g(-2)!=0,` and Rolles theorem is not applicable to `f(x)=(x^2-4)/(g(x))in[-2,2],t h e ng(x)` has at least one root in `(-2,2)dot` Statement 2: If `f(a)=f(b),t h e ng(x)` has at least one root in `(-2,2)dot` Statement 2: If `f(a)=f(b),` then Rolles theorem is applicable for `x in (a , b)dot`

A

Statement I is true, Statement II is also true, Statement II is the correct explanation of Statement I.

B

Statement I is true, Statement II is also true, Statement II is not the correct explanation of Statement I

C

Statement I is true, Statement II is false

D

Statement I is false, Statement II is true

Text Solution

Verified by Experts

The correct Answer is:
C
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Statement 1: If g(x) is a differentiable function, g(2)!=0,g(-2)!=0, and Rolles theorem is not applicable to f(x)=(x^2-4)/(g(x)), x in[-2,2],then g(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b),t h e ng(x) has at least one root in (-2,2)dot Statement 2: If f(a)=f(b), then Rolles theorem is applicable for x in (a , b)dot

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