Home
Class 12
MATHS
Verify Mean Value Theorem, if f(x) = x^3...

Verify Mean Value Theorem, if `f(x) = x^3-5x^2-3x`, in the interval [a, b], where a = 1 and b = 3. Find all `c in (1,3)` for which `f'(c) = 0`.

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    PSEB|Exercise Exercise|151 Videos

  • APPLICATION OF DERIVATIVES

    PSEB|Exercise Exercise|189 Videos

  • DETERMINANTS

    PSEB|Exercise Exercise|101 Videos

Similar Questions

Explore conceptually related problems

Verify Mean Value Theorem, if f(x) = x^2-4x-3 , in the interval [a, b], where a = 1 and b = 4.

Verify Rolle's theorem for the function : f(x) = x^3-4x in the interval [-2, 2]

Verify Rolle's theorem for f (x) = x^2 - 3x + 2, x in [1, 2]

Verify Roll's Theorem for the function f (x) = x^2+x-6 in the interval [-3,2]

Verify Roll's Theorem for the function f (x) = x^2-5x+9 in the interval [1,4].

Verify Roll's Theorem for the function f (x) = x^2-x-12 in the interval [-3,4].

Verify Rolle's Theorem for the function f(x) = x^2 + x - 6 in the interval [-3,2]

Verify Rolle's theorem for the function f(x)=x^(3)-3x^(2)+2x in the interval [0,2] .

PSEB-CONTINUITY AND DIFFERENTIABILITY-Exercise
  1. If f:[-5,5] rarr R is a differentiable function and if f'(x) does not...

    Text Solution

    |

  2. Verify Mean Value Theorem, if f(x) = x^2-4x-3, in the interval [a, b],...

    Text Solution

    |

  3. Verify Mean Value Theorem, if f(x) = x^3-5x^2-3x, in the interval [a,...

    Text Solution

    |

  4. Verify Mean Value Theorem, if f(x) = x^3-5x^2-3x, in the interval [a,...

    Text Solution

    |

  5. Differentiate w.r.t. x the function : (3x^2 - 9x + 5)^9

    Text Solution

    |

  6. Differentiate w.r.t. x the function : sin^3x + cos^6 x

    Text Solution

    |

  7. Differentiate w.r.t. x the function : (5x)^(3cos2x)

    Text Solution

    |

  8. Differentiate w.r.t. x the function : sin^-1(xsqrtx), 0lexle1

    Text Solution

    |

  9. Differentiate w.r.t. x the function : cos^-1(x/2)/sqrt(2x+7), x lies b...

    Text Solution

    |

  10. Differentiate w.r.t. x the function : cot^-1[(sqrt(1+sinx) + sqrt(1-si...

    Text Solution

    |

  11. Differentiate w.r.t. x the function : (logx)^logx, x>1

    Text Solution

    |

  12. Differentiate w.r.t. x the function : cos(acosx+bsinx), for some const...

    Text Solution

    |

  13. Differentiate w.r.t. x the function : (sinx - cosx)^(sinx-cosx), x lie...

    Text Solution

    |

  14. Differentiate w.r.t. x the function : x^x + x^a + a^x + a^a, for some ...

    Text Solution

    |

  15. Differentiate w.r.t. x the function : x^(x^2-3) + (x-3)^(x^2), for x>...

    Text Solution

    |

  16. Find dy/dx if y =12(1-cost), x =10(t-sint)

    Text Solution

    |

  17. Find dy/dx if y = sin^-1x + sin^-1 sqrt(1-x^2), 0ltxlt1

    Text Solution

    |

  18. If xsqrt(1+y) + ysqrt(1+x) = 0 for x lies between -1 and 1 prove that ...

    Text Solution

    |

  19. If (x-a)^2 + (y-b)^2 = c^2 , for some c > 0, prove that [1+(dy/dx)^2]...

    Text Solution

    |

  20. If cosy = xcos(a+y), with cos a ne +-1, prove that dy/dx = (cos^2(a+y...

    Text Solution

    |