Home
Class 12
MATHS
If f(x)=x^((2)/(3)), x in [-1,1], then...

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

A

f is differentiable in (-1,1)

B

f is not continuous on [1,-1]

C

`Rolle's theorem is applicable for f

D

Rolle's theorem is not applicable for f

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DEFINITEINTEGRAL

    NIKITA PUBLICATION|Exercise MULTIPLE CHOICE QUESTIONS:(MCQ)|27 Videos

  • BINOMIAL DISTRIBUTION

    NIKITA PUBLICATION|Exercise MCQS|77 Videos

Similar Questions

Explore conceptually related problems

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

f(x)=x^(2)-root(3)(|x|),x in[-1,1] Rollels theorem is not applicable because

Verify L.M.V.theorem for f(x)={2+x^(3),x 1 on [-1,2]

If f(x) = (1)/(2x-1) , x ne (1)/(2) , then show that : f(f(x)) = (2x-1)/(3-2x) , x ne (3)/(2)

Find the inverse of the function f(x) = In (x^2 + 3x + 1), x in [1, 3] and assuming it to be an onto function.

If f(x) is continuous at x=1 , where f(x)=((x+3x^(2)+5x^(3)+...+(2n-1)x^(n)-n^(2))/(x-1)) , for x !=1 , then f(1)=

If f(x)=(1+x)(1+x^2)(1+x^3)(1+x^4) , then f'(0)=1

If (f(x))/(x^(2)-x+1)-(1)/(f(x)) is the partial fraction of (3x)/(x^(3)+1) , then f(x) is__________.

NIKITA PUBLICATION-APPLICATIONS OF DERIVATIVES-MULTIPLE CHOICE QUESTIONS
  1. If f(x)=(x-1)(2x-3), x in [1,3], then

    Text Solution

    |

  2. If f(x)=(x-1)(x-2)(x-3), x in [1,3], then

    Text Solution

    |

  3. If f(x)=x^((2)/(3)), x in [-1,1], then

    Text Solution

    |

  4. If f(x)=|x|, x in [-2,2], then

    Text Solution

    |

  5. If f(x) = x^3 + bx^2 + ax satisfies the conditions on Rolle's theorem ...

    Text Solution

    |

  6. If the functio f(x)^(3)-6x^(2)+ax+b satisfies Rolle's theorem in the i...

    Text Solution

    |

  7. Verify Rolle's theorem for the following functions f(x) = sin x + cos ...

    Text Solution

    |

  8. If f(x)=e^(x) sin x, x in [0, pi], then

    Text Solution

    |

  9. A function f is defined by f(x)=x^(x) sin x in [0,pi]. Which of the fo...

    Text Solution

    |

  10. If the Rolle's theorem for f(x)=e^(x)(sin x-cosx) is verified on [(pi)...

    Text Solution

    |

  11. Verify Rolle's theorem for each of the following functions : f(x) = ...

    Text Solution

    |

  12. If Rolle's theorem holds for the function f(x) = (x - 2) log x, x in [...

    Text Solution

    |

  13. If Rolle's theorem holds for the function f(x) = (x - 2) log x, x in [...

    Text Solution

    |

  14. The equation x log x = 3-x has, in the interval (1,3) :

    Text Solution

    |

  15. Verify LMVT for the following function f(x)=x^2-3x-1, x in[-11/7, 13/7...

    Text Solution

    |

  16. Verify LMVT for the following functions: f(x)=x(2-x), x in [0, 1]

    Text Solution

    |

  17. If LMVT is applicable for f(x)=x(x+4)^(2), x in [0,4], then c=

    Text Solution

    |

  18. Find c if LMVT is applicable for f(x)=x(x-1)(x-2), x in [0, 1 /2]

    Text Solution

    |

  19. If mean value theorem holds for the function f(x)=(x-1)(x-2)(x-3), x i...

    Text Solution

    |

  20. From mean value theoren : f(b)-f(a)=(b-a)f^(prime)(x1); a lt x1 lt b...

    Text Solution

    |