Home
Class 12
MATHS
If the function f(x)=a x^3+b x^2+11 x-6 ...

If the function `f(x)=a x^3+b x^2+11 x-6` satisfies conditions of Rolles theorem in `[1,3] and f'(2+1/(sqrt(3)))=0,` then values of `a and b`, respectively, are

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

If the function f(x)=4x^(3)+ax^(2)+bx-1 satisfies all the conditions of Rolle's theorem in -(1)/(4) le x le 1 and if f'((1)/(2))=0 , then the values of a and b are -

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

If the function f(x)=x^(3)-ax^(2)+bx-6 defined in 1 le x le 3 satisfies Rolle's theorem when 1lt c lt 3 where c=2+(1)/(sqrt(3)) , find the values of a and b.

If the function f(x) stisfies the conditions of Rolle's theorem in [1, 2] and f'(x) is continuous in [1, 2], then int_(1)^(2)f'(x)dx is equal to -

Function f(x)=log(x^3+sqrt1+x^6) is

If f(x) satisfies the condition of Rolle's theorem in [1,2] , then int_1^2 f'(x) dx is equal to (a) 1 (b) 3 (c) 0 (d) none of these

If the function f(x)=x^(3)+ax^(2)-bx+4 defined in -2 le x le 2 satisfies Rolle's theorem when -2 lt c lt 2 where c=(1)/(3)(1+sqrt(13)) , then find the values of a and b.

If the function f(x) satisfies the condition f(x + 1/x) = x^2 + 1/x^2,x ne 0 then f(x) is

If the conditions of Rolle's theorem are satisfied by the function f(x)=x^(3)+ax^(2)+bx-5 in 1 le x le 3 with c=2+(1)/(sqrt(3)) , then the values of a and b are -

Consider the function f(x)=8x^2-7x+5 on the interval [-6,6] .the value of c that satisfies the condition of the mean value theorem is

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The value of c in Lagranges theorem for the function f(x)=logsinx in t...

    Text Solution

    |

  2. Prove that ln(1+x) < x for x > 0.

    Text Solution

    |

  3. If the function f(x)=a x^3+b x^2+11 x-6 satisfies conditions of Rolles...

    Text Solution

    |

  4. Prove that |cosalpha-cosbeta|lt=|alpha-beta|

    Text Solution

    |

  5. A value of 'c' for which the conclusion of mean value theorem holds fo...

    Text Solution

    |

  6. If a , b > 0 a n d 0 < p < 1, then prove that (a+b)^p < a^p+b^pdot

    Text Solution

    |

  7. Each question has four choices, a,b,c and d, out of which only one is ...

    Text Solution

    |

  8. Let fa n dg be differentiable on R and suppose f(0)=g(0)a n df^(prime)...

    Text Solution

    |

  9. The abscissa of the point on the curve sqrt(x y)=a+x the tangent at wh...

    Text Solution

    |

  10. For 0ltxltpi/ 2, prove that cos(sinx)gtsin(cosx)

    Text Solution

    |

  11. In which of the following functions is Rolles theorem applicable? (a)f...

    Text Solution

    |

  12. Show that x/(1+x)ltlog(1+x)ltxforallxgt0.

    Text Solution

    |

  13. A point on the parabola y^2=18 x at which the ordinate increases at t...

    Text Solution

    |

  14. Prove that e^x+sqrt(1+e^(2x))geq(1+x)+sqrt(2+2x+x^2)AAx in R

    Text Solution

    |

  15. Determine the local maxima and local minima of f(x)=(x+1)^2(x-1)^3 is

    Text Solution

    |

  16. Let g(x)=f(logx)+f(2-logx)a n df''(x)<0AAx in (0,3)dot Then find the i...

    Text Solution

    |

  17. Prove that The maximum value of (sqrt(-3+4x-x^2)+4)^2+(x-5)^2(w h e r ...

    Text Solution

    |

  18. Find the points of inflection for (a)f(x)=sinx (b)f(x)=3x^4-4x^3

    Text Solution

    |

  19. Statement 1: If both functions f(t)a n dg(t) are continuous on the clo...

    Text Solution

    |

  20. Discuss monotonocity of y=f(x) which is griven by x=1/(1+t^2) and y=1...

    Text Solution

    |