Home
Class 12
MATHS
If the function f(x)=4x^(3)+ax^(2)+bx-1...

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 -

A

`a=2, b=3`

B

`a=1,b=-4`

C

`a=-1, b=4`

D

`a=-4, b=-1`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 6|80 Videos
  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 8|80 Videos
  • MCQ ZONE

    CHHAYA PUBLICATION|Exercise Question Paper 3|80 Videos
  • MAXIMA AND MINIMA

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination E|2 Videos
  • MCQ ZONE 3

    CHHAYA PUBLICATION|Exercise Question Paper 8|30 Videos

Similar Questions

Explore conceptually related problems

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

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)=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 -

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 -

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 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) is defined by f(x)=(x(x+1))/(e^(x)) in [-1, 1], then the values of c in Rolle's theorem is -

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 f(x)=ax^(2)+bx+c and f(x - 1) = f(x) + 2x + 1. then find the values of a and b.

CHHAYA PUBLICATION-MCQ ZONE -Question Paper 4
  1. If x=sin t and y=cos p t, then which of the following is true ?

    Text Solution

    |

  2. In the mean value theorem f(b)-f(a)=(b-a)f'(c )(a lt c lt b), if a=4,...

    Text Solution

    |

  3. If the function f(x)=4x^(3)+ax^(2)+bx-1 satisfies all the conditions ...

    Text Solution

    |

  4. The value of lim(x to 0)(e^(x)-log(e+ex))/(x) is -

    Text Solution

    |

  5. Let f(x) ={{:((1-sin x)/(pi-2x)",","when" x ne (pi)/(2)),(lamda ",","w...

    Text Solution

    |

  6. If (sqrt(x))^((sqrt(x))^((sqrt(x))^(...oo))) and x(dy)/(dx) =(f(y))/...

    Text Solution

    |

  7. If x=e^(t)sint and y=e^(t)cost, then the value of (x+y)^(2)(d^(2)y)...

    Text Solution

    |

  8. If y=f(x^(2)) and f'(x)=sqrt(3x^(2)+1) then the value of (dy)/(dx) a...

    Text Solution

    |

  9. If x=sec theta-cos theta, y =sec^(n)theta-cos^(n) theta and (x^(2)+4...

    Text Solution

    |

  10. If f(x) is a differentiable function for all x gt 0 and lim(y to x)(y...

    Text Solution

    |

  11. If y^(2)=4ax, then the value of (d^(2)y)/(dx^(2))*(d^(2)x)/(dy^(2)) i...

    Text Solution

    |

  12. The value of lim(n to oo) (1^(p)+2^(p)+3^(p)+…+n^(p))/(n^(p+1)) is -

    Text Solution

    |

  13. The value of int(0)^(1.5)[x^(2)]dx is -

    Text Solution

    |

  14. If I(n)=int(0)^((pi)/(4)) tan^(n)x dx, then the value of lim(n to oo...

    Text Solution

    |

  15. The value of int(0)^((pi)/(2)) (sinx dx)/(sin x+cos x) is equal to -

    Text Solution

    |

  16. The value of the integral int(-(pi)/(7))^((pi)/(7))x^(3)sin^(2)x dx is...

    Text Solution

    |

  17. int"cosec"^(4)x dx is equal to -

    Text Solution

    |

  18. The value of int(dx)/(2sqrt(x)(x+1)) is -

    Text Solution

    |

  19. The value of the integral int(0)^(1) (dx)/( x^(2)+2x cos alpha +1) is...

    Text Solution

    |

  20. Let (d)/(dx) F(x)=(e^(sin x))/(x), x gt 0, If int(1)^(4) (3)/(x) ...

    Text Solution

    |