Home
Class 12
MATHS
It is given that for the function f(x...

It is given that for the function `f(x)=x^3-6x^2+a x+b` on `[1,\ 3]` , Rolles theorem holds with `c=2+1/(sqrt(3))` . Find the values of `a` and `b` , if `f(1)=f(3)=0` .

Text Solution

Verified by Experts

Given` f(1)=f(3)=0`
`1^3−6×1+a+b=3^3−6×3^2+3a+b=0`
`\Rightarrow a+b−5=0 and 3a+b−27=0`
on solving ...
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

it is given for the function f(x)=x^(3)-6x^(2)+ax+b on [1,3], Rolle's theorem holds with c=2+(1)/(sqrt(3)). Find the values of a and b if f(1)=f(3)=0

It is given that for the function f(x)=x^(3)-6x^(2)+ax+b on [1,3], Rolles theorem holds with c=2+(1)/(sqrt(3)). Find the values of a and b, if f(1)=f(3)=0

It is given that for the function f given by f(x)=x^(3)+bx^(2)+ax,x in[1,3]. Rolles theorem holds with c=2+(1)/(sqrt(3)). Find the values of a and b

If the function f(x)=x^(3)-6x^(2)+ax+b defined on [1,3] satisfies Rolles theorem for c=(2sqrt(3)+1)/(sqrt(3)) then find the value of a and b

If Rolle's theorem holds for the function f(x) = x^(3) + bx^(2) + ax + 5 on [1, 3] with c = (2 + (1)/(sqrt3)) , find the value of a and b

It is given that the Rolles theorem holds for the function f(x)=x^3+b x^2+c x ,\ \ x in [1,2] at the point x=4/3 . Find the values of b and c .

It is given that the Rolles theorem holds for the function f(x)=x^(3)+bx^(2)+cx,x in[1,2] at the point x=(4)/(3). Find the values of b and c

Verify mean value theorem for the function f(x) = x^(3)-2x^(2)-x+3 in [0,1]

Verify Rolles theorem for function f(x)=x^(2)-4x+3 on [1,3]

RD SHARMA-MEAN VALUE THEOREMS-Solved Examples And Exercises
  1. Verify Rolles theorem for the function: f(x)=x(x+3)e^(-x//2) on [-3...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  7. Discuss the applicability of Rolles theorem for the function f(x)=[...

    Text Solution

    |

  8. Discuss the applicability of Rolles theorem for the function f(x)=s...

    Text Solution

    |

  9. Discuss the applicability of Rolles theorem for the function f(x)=2...

    Text Solution

    |

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

    Text Solution

    |

  11. Verify Rolles theorem for function f(x)=x^2-8x+12 on [2,\ 6]

    Text Solution

    |

  12. Verify Rolles theorem for function f(x)=x^2-4x+3 on [1,\ 3]

    Text Solution

    |

  13. Verify Rolles theorem for function f(x)=(x-1)(x-2)^2 on [1,\ 2]

    Text Solution

    |

  14. Verify Rolles theorem for function f(x)=x(x-1)^2 on [0,\ 1]

    Text Solution

    |

  15. Verify Rolles theorem for function f(x)=(x^2-1)(x-2) on [-1,\ 2]

    Text Solution

    |

  16. Verify Rolles theorem for function f(x)=x(x-4)^2 on [0,\ 4]

    Text Solution

    |

  17. Verify Rolles theorem for function f(x)=x(x-2)^2 on [0,\ 2]

    Text Solution

    |

  18. Verify Rolles theorem for function f(x)=x^2+5x+6 on [-3,\ -2]

    Text Solution

    |

  19. Verify Rolles theorem for function f(x)=cos2(x-pi//4) on [0,\ pi//2...

    Text Solution

    |

  20. Verify Rolles theorem for function f(x)=sin2x on [0,\ pi//2]

    Text Solution

    |