Home
Class 12
MATHS
Find the value of a for which the functi...

Find the value of a for which the function `f(x)=ax^(3)-3(a+2)x^(2)+9(a+2)x-1` is decreasing.

Text Solution

Verified by Experts

The correct Answer is:
`a lt -2`
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|83 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK|51 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise MISCELANEOUS EXERCISE - 6|27 Videos

  • ANNUAL EXAMINATION :SAMPLE PAPER

    KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos

  • APPLICATION OF INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

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

Find the values of x for which the functions f(x)= 3x^(2)-1 and g(x)= 3 + x are equal

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

Find the intervals in which function f given by f(x)=2x^(3)-3x^(2)-36x+7 is (a) increasing (b) decreasing

Find the domain of the function f(x)=(x^(2)+3x+5)/(x^(2)-5x+4)

Find the intervals in which the function f given f(x)=x^(3)+(1)/(x^(3)), x ne 0 is (i) increasing (ii) decreasing.

Find the derivative at x = 2 of the function f(x) = 3x .

Find the intervals in which the function f given by f(x)=2x^(2)-3x is (a) incresing (b) decreasing

Find the least value of a such that the function given by f(x)=x^(2)+ax+1 is strictly increasing on (1, 2).

Find the value of a for which the polynomial 3x^(3)+14x^(2)+9x+a is divisible by 3x+5 .

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -PRACTICE WORK
  1. Find the least value of a such that the function given by f(x)=x^(2)+a...

    Text Solution

    |

  2. Prove that f(x)=x^(2)-x sin x is increasing on (0, (pi)/(2)).

    Text Solution

    |

  3. Find the value of a for which the function f(x)=ax^(3)-3(a+2)x^(2)+9(a...

    Text Solution

    |

  4. Find the in intervals in which f(x)=sin^(4)x+cos^(4)x is increasing or...

    Text Solution

    |

  5. f : (0, pi)to R, f(x)=2x+cot x. Find the intervals in which f(x) is st...

    Text Solution

    |

  6. Show that f(x)=x^(3)-3x^(2)+4x, x in R is strictly increasing on R.

    Text Solution

    |

  7. Without using differentiation, prove that f(x)=ax+b, where a gt 0 is s...

    Text Solution

    |

  8. f : R^(+)to R^(+), f(x)=(log x)/(sqrt(x)). Find the intervals in which...

    Text Solution

    |

  9. Find the equation of the tangent to the curve y^(2)=16x which is paral...

    Text Solution

    |

  10. Find the equation of the normal to the curve y = 8x which is perpendic...

    Text Solution

    |

  11. Prove that the curves x^(2)+y^(2)=ax and x^(2)+y^(2)=by are cuts ortho...

    Text Solution

    |

  12. Find the equation of the tangent and normal to the curve y^(2)(a+x)=x^...

    Text Solution

    |

  13. Show that the normal to the curve 5x^(5)-10x^(3)+x+2y+6=0 at P(0,-3) i...

    Text Solution

    |

  14. Show that a point at which the line (x)/(a)+(y)/(b)=1 touches to the c...

    Text Solution

    |

  15. A line x cos alpha + y sin alpha = P is a tangent to the curve (x^(2))...

    Text Solution

    |

  16. Find the equations of the tangent to the curve y=cos(x+y) which is par...

    Text Solution

    |

  17. Find the points on the curve x^(2)y^(2)+xy=2 at which the slope of the...

    Text Solution

    |

  18. The slope of the tangent to the curve xy+ax+by=2 at a point (1, 1) the...

    Text Solution

    |

  19. Prove that all points on the curve y^(2)=4a[x+a sin((x)/(a))] at which...

    Text Solution

    |

  20. Find the equation of the normal to the curve y=(1+x)^(y)+sin^(-1)(sin^...

    Text Solution

    |