Home
Class 12
MATHS
Prove that the function f(x)=x^(3)-6x^(2...

Prove that the function `f(x)=x^(3)-6x^(2)+12 x-18` is increasing for all `x in RR`.

Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTION

    CHHAYA PUBLICATION|Exercise Exercise 15 : Long Answer Type Questions|16 Videos

  • INCREASING AND DECREASING FUNCTION

    CHHAYA PUBLICATION|Exercise MCQ|5 Videos

  • INCREASING AND DECREASING FUNCTION

    CHHAYA PUBLICATION|Exercise Exercise 15 : Very short Answer Type Questions|13 Videos

  • IDENFINITE INTEGRAL

    CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Comprehension Type )|6 Videos

  • INTEGRALS OF SOME SPECIAL FORM OF FUNCTIONS

    CHHAYA PUBLICATION|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

Prove that the function f(x)=x^(3)-x^(2) is neither increasing nor decreasing in -2/3 lt x lt 2/3 .

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

Find the condition so that the function f(x)=x^(3)+ax^(2)+bx+c is an increasing function for all real values of x.

The function f(x) = ax + b is strictly increasing for all real x if

Prove that the function f(x)=(log)_e(x^2+1)-e^(-x)+1 is strictly increasing AAx in Rdot

Prove that the function f: RR rarr RR defined by, f(x)=sin x , for all x in RR is neither one -one nor onto.

Show that, the function 4x^(2)-6x-11 is increasing at x=4 and the function x^(2)/(x^(2)+16) is decreasing at x=-2 .

If f(x) = x^(3) - 6x^(2) + 9x +3 be a decreasing function, then x lies in-

If f(x+y)=f(x)dotf(y) for all real x , ya n df(0)!=0, then prove that the function g(x)=(f(x))/(1+{f(x)}^2) is an even function.

Find the intervals in which the function f given by f (x) = 4x^(3) – 6x^(2) – 72x + 30 is (a) increasing (b) decreasing.

CHHAYA PUBLICATION-INCREASING AND DECREASING FUNCTION-Exercise 15 : Short Answer Type Questions
  1. Prove that the function f(x)=x+1/x (x ne 0) is decreasing for all x in...

    Text Solution

    |

  2. Find the intervals in which the following functions are (a) increasing...

    Text Solution

    |

  3. Find the intervals in which the following functions are (a) increasing...

    Text Solution

    |

  4. Find the intervals in which the following functions are (a) increasing...

    Text Solution

    |

  5. 24. Find the intervals in which the following function is (a) increasi...

    Text Solution

    |

  6. 24. Find the intervals in which the following function is (a) increasi...

    Text Solution

    |

  7. Find the intervals in which the following functions are (a) increasing...

    Text Solution

    |

  8. Find the intervals in which the function f(x)=sin x-cos x where 0 lt x...

    Text Solution

    |

  9. Find the intervals in which the function f(x)=sin x-cos x where 0 lt x...

    Text Solution

    |

  10. Prove that the function f(x)=x^(3)-6x^(2)+12 x-18 is increasing for al...

    Text Solution

    |

  11. Prove that the function f(x)=x^2-x+1 is neither increasing nor decr...

    Text Solution

    |

  12. Find the intervals in which f(x)=2x^3-24 x+7 is increasing or decreasi...

    Text Solution

    |

  13. If f(x)=(x-1) e^(x)+1, show that f(x) is positive for all positive val...

    Text Solution

    |

  14. Prove that, the function 5+24x+3x^(2)-x^(3) increases in the interval ...

    Text Solution

    |

  15. If f(theta)=theta sin theta+cos theta, show that, f(theta) steadily in...

    Text Solution

    |

  16. Find the intervals in which f(x)=(x+2) e^(-x) is increasing

    Text Solution

    |

  17. Find the intervals in which f(x)=(x+2) e^(-x) is decreasing

    Text Solution

    |

  18. Find the intervals in which f(x)=(x-1)^3(x-2)^2 is increasing or decre...

    Text Solution

    |

  19. Find the intervals in which f(x)=(x-1)^3(x-2)^2 is increasing or decre...

    Text Solution

    |

  20. Prove that the function f(x)=x^3-6x^2+12 x-18 is increasing on R .

    Text Solution

    |