Home
Class 12
MATHS
Rolles theorem is applicable for...

Rolles theorem is applicable for

A

`f(x)=|x|` on `[-1, 1]`

B

f(x) = [x] for x ∈ [5, 9]

C

`f(x) = x^2 – 1 x ∈ [1, 2]`

D

NOne of these

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MEAN AND VARIANCE OF A RANDOM VARIABLE

    RD SHARMA|Exercise Solved Examples And Exercises|113 Videos

  • PROBABILITY

    RD SHARMA|Exercise Solved Examples And Exercises|422 Videos

Similar Questions

Explore conceptually related problems

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

Let Rolle's theorem is applicable for f(x)=x^(3)+ax^(2)+beta x+2 where x in[0,2] and the value of c= (1)/(2) then (a+2 beta) is

Let f(x)=Max .{x^(2),(1-x)^(2),2x(1-x)}wherexin[0,1] If Rolle's theorem is applicable for f(x) on largestpossible interval [a,b] then the value of 2(a+b+c) when c in[a,b] such that f(c)=0, is

Consider the function g/defined by g(x) = {x^2 sin(pi/x) +(x-1)^2sin(pi/(x-1)),x!=0,1; 0, if x=0,1} then which of the following statement(s) is/are correct? (A) g (x) is differentiable AA in R. (B) g(x) is discontinuous at x=0 but continuous at x = 1 . C) g(x) is discontinuous at both x =0 and x = 1 D) Rolle's theorem is applicable for g(x) in [0, 1].

Consider f(x)=|1-x| 1 lt=xlt=2 a n d g(x)=f(x)+bsinpi/2 x , 1 lt=xlt=2 Then which of the following is correct? Rolles theorem is applicable to both f, g a n d b = 3//2 LMVT is not applicable of f and Rolles theorem if applicable to g with b=1/2 LMVT is applicable to f and Rolles theorem is applicable to g with b = 1 Rolles theorem is not applicable to both f,g for any real b .

If Rolle's theorem is applicable to the function f(x)=a cos(x+b)+c in [(pi)/(8),(pi)/(4)], then b may be equal to (Here a!=0)

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

Let f(x)=x^4-6x^3+12 x^2-8x+3. If Rolles theorem is applicable to varphi(x) on [2,2+h] and there exist c in (2,2+h) such that varphi^(prime)(c)=0 and (f(2+h)-f(2))/(h^3)=g(c), then

RD SHARMA-MEAN VALUE THEOREMS-Solved Examples And Exercises
  1. Verify Rolle's theorem for each of the following functions on indicate...

    Text Solution

    |

  2. Verify Rolle theorem for the function f(x)=log{(x^2+a b)/(x(a+b))}on[a...

    Text Solution

    |

  3. Rolles theorem is applicable for

    Text Solution

    |

  4. Discuss the applicability of Rolles theorem for the function f(x)=3...

    Text Solution

    |

  5. Discuss the applicability of Rolles theorem for f(x)=tanx on [0,\ p...

    Text Solution

    |

  6. Discuss the applicability of Rolle's theorem on the function f(x...

    Text Solution

    |

  7. Verify Rolles theorem for the function f(x)=x^2-5x+6 on the interva...

    Text Solution

    |

  8. Verify Rolles theorem for the function f(x)=x(x-3)^2,\ 0lt=xlt=3 .

    Text Solution

    |

  9. Verify Rolles theorem for the function f(x)=x^3-6x^2+11 x-6 on the ...

    Text Solution

    |

  10. Verify Rolles theorem for the function f(x)=(x-a)^m(x-b)^n on the i...

    Text Solution

    |

  11. Verify Rolles theorem for the function f(x)=sqrt(4-x^2) on [-2,\ 2]...

    Text Solution

    |

  12. Verify Rolles theorem for the function f(x)=log{(x^2+a b)/(x(a+b))}...

    Text Solution

    |

  13. Verify Rolles theorem for the function: f(x)=s in^2x on 0lt=xlt=pi

    Text Solution

    |

  14. Verify Rolles theorem for the function: f(x)=sinx+cosx-1 on [0,\ pi...

    Text Solution

    |

  15. Verify Rolles theorem for the function: f(x)=sinx-sin2x on [0,\ pi]

    Text Solution

    |

  16. Verify Rolles theorem for the function: f(x)=x(x+3)e^(-x//2) on [-3...

    Text Solution

    |

  17. Verify Rolles theorem for the function: f(x)=e^x(sinx-cosx) on [pi/...

    Text Solution

    |

  18. It is given that for the function f(x)=x^3-6x^2+a x+b on [1,\ 3] , ...

    Text Solution

    |

  19. It is given that for the function f given by f(x)=x^3+b x^2+a x , x...

    Text Solution

    |

  20. Find the point on the curve y=cosx-1,\ \ x in [pi/2,(3pi)/2] at whi...

    Text Solution

    |