Home
Class 12
MATHS
The interval to which a may belong so th...

The interval to which a may belong so that the function `f(x)=(1-(sqrt(21-4a-a^2))/(a+1))x^3+5x+100` is increasing for `x in R`

Text Solution

Verified by Experts

The correct Answer is:
`[-7,-1) uu[2,3]`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    RESONANCE|Exercise Exersise-3 Part II|22 Videos

  • COMBINATORICS

    RESONANCE|Exercise Exercise-2 (Part-II: Previously Asked Question of RMO)|8 Videos

Similar Questions

Explore conceptually related problems

Prove that the function given by f(x)=x^(3)-3x^(2)+3x-100 is increasing in R .

Show that the function f(x)= x^(3) - 3x^(2)+3x - 1 is an increasing function on R.

The interval in which the function f(x)=x^(e^(2-x)) increases is

The interval on which the function f(x)=-2x^(3)-9x^(2)-12x+1 is increasing is :

Find the interval in which the function f(x) =cos^(-1) ((1-x^(2))/(1+x^(2))) is increasing or decreasing.

Prove that the function f(x)=x^(3)-3x^(2)+3x-100 is increasing on R .

Find the domain of the function f(x) = sqrt(log_(1//4) ((5x - x^(2))/(4)))

Prove that the function f(x)=2x^(3)-21x^(2)+36x-40 is strictly increasing in the interval (-oo, 1) .

Find the interval in which the function f(x)=2x^(3)-21x^(2)+36x-40 is increasing or decreasing.

RESONANCE-APPLICATION OF DERIVATIVES-High Level Problems (HLP)
  1. lf f'(x) > 0,f"(x)>0AA x in (0,1) and f(0)=0,f(1)=1,then prove that...

    Text Solution

    |

  2. find the interval of increasing and decreasing for the function g...

    Text Solution

    |

  3. The interval to which a may belong so that the function f(x)=(1-(sqrt(...

    Text Solution

    |

  4. Find positive real numbers 'a' and 'b' such that f(x) =ax-bx^(3) has...

    Text Solution

    |

  5. For any acute angled DeltaABC find the maximum value of (sin A)/(A) +(...

    Text Solution

    |

  6. For what real values of a' and 'b' all the extrema of the function f(x...

    Text Solution

    |

  7. Find the minimum value of f(x) =8^(x) +8^(-x) -4(4^(x)+4^(-x)) , AA x ...

    Text Solution

    |

  8. Show that height of the cylinder of greatest volume which can be insc...

    Text Solution

    |

  9. Find the cosine of the angle at the vertex of an isoceles triangl...

    Text Solution

    |

  10. A tangent to the curve y=1 -x^(3) is drawn so that the abscissa x(0)...

    Text Solution

    |

  11. A cone is made from a circular sheet of radius sqrt3 by cutting out a ...

    Text Solution

    |

  12. Find the minimum distance of origin from the curve ax^(2) +2bxy+ay^(2)...

    Text Solution

    |

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

    Text Solution

    |

  14. Find which of the two larger en (1+x) " or " (tan^(-1)x)/(1+x).

    Text Solution

    |

  15. Let f'(sin x) lt 0 and f''(sin x) gt 0 AA x in (0, pi/2) and g (x) =...

    Text Solution

    |

  16. Let f(x)a n dg(x) be differentiable functions such that f^(prime)(x)g(...

    Text Solution

    |

  17. f is continuous in [a, b] and differentiable in (a, b) (where a>0 ) su...

    Text Solution

    |

  18. Find all the values of the parameter'a' for which the function; f(x)=...

    Text Solution

    |

  19. Let h be a twice continuously differentiable positive function on an o...

    Text Solution

    |

  20. if the complete set of values (s) of 'a' for which the function f (x)...

    Text Solution

    |