Home
Class 12
MATHS
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
Promotional Banner

Topper's Solved these Questions

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Passage Based Questions)|8 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (Matching Type Questions)|1 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • DIFFERENTIATION

    ARIHANT MATHS|Exercise Exercise For Session 10|4 Videos

  • ELLIPSE

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|27 Videos

Similar Questions

Explore conceptually related problems

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] .

Rolle's theorem is not applicable to the function f(x) =|x| defined on [-1,1] because

prove that the roll's theorem is not applicable for the function f(x)=2+(x-1)^((2)/(3)) in [0,2]

For the function f(x) = e^(cos x) , Rolle's theorem is applicable when

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

Show that Rolle's theorem is not applicable fo rthe following functions: f(x)=x^(3), interval [-1,1]

The value of c in Rolle's theorem for the function f(x)=(x(x+1))/(e^(x)) defined on [-1,0] is