Home
Class 12
MATHS
Verify the Rolle's theorem for each of t...

Verify the Rolle's theorem for each of the function in following questions:
`f(x)= x(x-1)^(2), " in" x in [0, 1]`

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(3) in (0, 1)`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise NCERT Exemplar Problems and Solution (Long Answer Type Questions)|10 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise NCERT Exemplar Problems and Solution (Objective Type Questions)|28 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    KUMAR PRAKASHAN|Exercise Textbook Illustrations for Practice Work|96 Videos

  • BOARD'S QUESTION PAPER MARCH - 2020

    KUMAR PRAKASHAN|Exercise PART - B (Section - C)|4 Videos

  • DETERMINANTS

    KUMAR PRAKASHAN|Exercise Practice Paper-4 (Section-D)|2 Videos

Similar Questions

Explore conceptually related problems

Verify the Rolle's theorem for each of the function in following questions: f(x)= sqrt(4-x^(2)), "in " x in [-2, 2]

Verify the Rolle's theorem for each of the function in following questions: f(x)= x(x+3).e^(-(x)/(2)), "in" x in [-3, 0]

Verify the Rolle's theorem for each of the function in following questions: f(x)= log (x^(2)+2)- log 3, " in " x in [-1, 1]

Verify the Rolle's theorem for each of the function in following questions: f(x)= sin^(4)x + cos^(4)x, "in " x in [0, (pi)/(2)]

Verify Rolle's theorem for the following functions: f(x)= x(x-3)^(2), x in [0, 3]

Verify Rolle's theorem for the following functions: f(x)= sin x + cos x - 1, x in [0, (pi)/(2)]

KUMAR PRAKASHAN-CONTINUITY AND DIFFERENTIABILITY-NCERT Exemplar Problems and Solution (Short Answer Type Questions)
  1. If x= e^((x)/(y)), then prove that (dy)/(dx)= (x-y)/(x.log x)

    Text Solution

    |

  2. If y^(x)= e^(y-x), then prove that (dy)/(dx)= ((1+ log y)^(2))/(log y)

    Text Solution

    |

  3. If y= (cos x)^((cos x)^((cos x)……oo)), then show that (dy)/(dx)= (y^(2...

    Text Solution

    |

  4. If x sin (a + y) + sin a cos (a + y)= 0, then prove that (dy)/(dx)= (s...

    Text Solution

    |

  5. If sqrt(1-x^(2)) + sqrt(1 -y^(2))= a(x-y), then prove that (dy)/(dx)= ...

    Text Solution

    |

  6. If y= tan^(-1)x, then find (d^(2)y)/(dx^(2)) in terms of y alone.

    Text Solution

    |

  7. Verify the Rolle's theorem for each of the function in following quest...

    Text Solution

    |

  8. Verify the Rolle's theorem for each of the function in following quest...

    Text Solution

    |

  9. Verify the Rolle's theorem for each of the function in following quest...

    Text Solution

    |

  10. Verify the Rolle's theorem for each of the function in following quest...

    Text Solution

    |

  11. Verify the Rolle's theorem for each of the function in following quest...

    Text Solution

    |

  12. Discuss the applicability of Rolle's theorem on the function given by ...

    Text Solution

    |

  13. Find the points on the curve y= cos x-1 in x in [0, 2pi], where the ta...

    Text Solution

    |

  14. Using Rolle's theorem, find the point on the curve y= x (x-4), x in [0...

    Text Solution

    |

  15. Verify mean value theorem for each of the functions: f(x) = (1)/(4x-...

    Text Solution

    |

  16. Verify mean value theorem for each of the functions: f(x)= x^(3)-2x...

    Text Solution

    |

  17. Verify mean value theorem for each of the functions: f(x)= sin x- s...

    Text Solution

    |

  18. Verify mean value theorem for each of the functions: f(x)= sqrt(25-...

    Text Solution

    |

  19. Find a point on the curve y= (x-3)^(2), where the tangent is parallel ...

    Text Solution

    |

  20. Using mean value theorem, prove that there is a point on the curve y= ...

    Text Solution

    |