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`

Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 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.

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Find the greatest and the least values of the following functions i...

    Text Solution

    |

  2. If b > a, find the minimum value of |(x-a)^3+|(x-b)^3|, x in R

    Text Solution

    |

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

    Text Solution

    |

  4. If f(x)=2e^x-ae^(-x)+(2a+1)x-3 monotonically increases for AA x in R,...

    Text Solution

    |

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

    Text Solution

    |

  6. Using L M V T prove that tanx > x in (0,pi/2),

    Text Solution

    |

  7. For what value of adot,\ a n d\ b does the function f(x)={3\ \ ...

    Text Solution

    |

  8. If f is a continuous function on the interval [a,b] and there exists ...

    Text Solution

    |

  9. Prove that following inequalities sinxlt=xlt=tanx\ AA\ in [0,pi/2...

    Text Solution

    |

  10. Find the intervals of monotonicity of the following f(x)=2x^2-"ln"|...

    Text Solution

    |

  11. Let f(x) be a increasing function defined on (0,\ oo)dot If f...

    Text Solution

    |

  12. Prove that f(x)=x/(sinx) is an increasing function while g(x)=x/...

    Text Solution

    |

  13. Let f(x)=x^3+2x^2+x+5. Show that f(x)=0 has only one real roo...

    Text Solution

    |

  14. Prove that ln (1+1/x) gt (1)/(1+x), x gt 0. Hence, show that the fun...

    Text Solution

    |

  15. For what values of a , does the function f(x)=((sqrt(a+5))/(1-a)...

    Text Solution

    |

  16. The minimum value of the function f(x)=x^(3//2)+x^(-3//2)-4(x+1/x) ...

    Text Solution

    |

  17. Prove that tan^2x+6lns e c x+2cosx+4>6secx for x\ in ((3pi)/2,\...

    Text Solution

    |

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

    Text Solution

    |

  19. f(x) and g(x) are differentiable functions for 0 <= x <= 2 such that f...

    Text Solution

    |

  20. Consider the function f(x)={xsinpi/x ,forx >0 0,forx=0 The, the numb...

    Text Solution

    |