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

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`

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)=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 x= 3+ 2sqrt2 then find the value of x+1/x .

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 x= sqrt3+sqrt2 ,find the value of x^3-1/x^3 .

If x = 1/(2-sqrt3) then find the value of (x^(3) -2x^(2) -7x+2)

If x = 1/(2-sqrt3) then find the value of (x^(3) -2x^2 - 7x +4)

If x = 3 + 2 sqrt2 , then find the value of x + (1)/(x)

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

x^2+sqrt(3).f(x)+2sqrt(3)-3=0 , then the value of f(sqrt(3))

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. How many roots of the equation (x-1)(x-2)(x-3) + (x-1)(x-2)(x-4) + (x-...

    Text Solution

    |

  2. A window is in the form of a rectangle surmounted by a semicircular...

    Text Solution

    |

  3. If the function f(x)=x^3-6x^2+a x+b defined on [1,3] satisfies Rolles ...

    Text Solution

    |

  4. Draw the graph of f(x)=|(x^2-2)/(x^2-1)| .

    Text Solution

    |

  5. Find the intervals in which the following functions are increasing or ...

    Text Solution

    |

  6. Two towns Aa n dB are 60 km apart. A school is to be built to serve 1...

    Text Solution

    |

  7. Let f(x) be differentiable function and g(x) be twice differentiable f...

    Text Solution

    |

  8. Find the range of f(x)(x^2-x+1)/(x^2+x+1)

    Text Solution

    |

  9. Show that between any two roots of e^(-x)-cosx=0, there exists at leas...

    Text Solution

    |

  10. Discuss the maxima and minima points of f(x)=2x^3-3x^2-12 x+15

    Text Solution

    |

  11. If 2a+3b+6c=0 then the equation ax^2+bx+c=0 has in the interval (0,1)

    Text Solution

    |

  12. A figure is bounded by the curves y=x^2+1, y=0,x=0,a n dx=1. At what p...

    Text Solution

    |

  13. If the equation a x^2+b x+c=0 has two positive and real roots, then pr...

    Text Solution

    |

  14. Find the minimum length of radius vector of the curve (a^2)/(x^2)+(b^...

    Text Solution

    |

  15. Let P(x) be a polynomial with real coefficients such that P(sin^2x)=P(...

    Text Solution

    |

  16. Show that the cone of the greatest volume which can be inscribed in a ...

    Text Solution

    |

  17. If the curve y=a x^2-6x+b pass through (0,2) and has its tangent paral...

    Text Solution

    |

  18. Find the point at which the slope of the tangent of the function f(x)=...

    Text Solution

    |

  19. Find the equation of the tangent to the curve (1+x^2)y=2-x , where it ...

    Text Solution

    |

  20. An electric light is placed directly over the centre of a circular plo...

    Text Solution

    |