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Statement I If g(x) is a differentiable ...

Statement I If g(x) is a differentiable function `g(1) ne0, g(-1)ne0 ` and Rolle's theorem is not applicable to `f(x)=(x^(2)-1)/(g(x))` in `[-1, 1]`, then g(x) has atleast one root in `(-1, 1)`.
Statement II if `f(a)=f(b)`, then Rolle's theorem is applicable for `x in (a, b)`.

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))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

Rolle's theorem is applicable for the function f(x) = |x-1| in [0,2] .

Knowledge Check

  • Rolle 's theorem is not applicable for the function f(x)=|x| in the interval [-1,1] because

    A
    f'(1) does not exist
    B
    f'(-1) does not exist
    C
    f(x) is discontinuous at x=0
    D
    f' (0) does not exist

  • Rolle’s theorem is not applicable for the function f(x)= |x| in the interval , [-1,1] because

    A
    f'(1) does not exist
    B
    f'(-1) does not exist
    C
    f(x) is discontinuous at x = 0
    D
    f`(0) does not exist

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