Home
Class 12
MATHS
The function f(x)=x^(3)-3x^(2)+6 is an i...

The function `f(x)=x^(3)-3x^(2)+6` is an increasing funciton for :

A

`0 lt x lt 2`

B

`x lt2`

C

`x gt 2 or x gt 0`

D

all x

Text Solution

Verified by Experts

The correct Answer is:
C
For increasing funciton
f(x)`=3x^(2)-65xgt0`
`rarr x(x-2) gt 0`
Either both fctor s x nd (-2) are simultaneously +ve simultaneously -ve
Case I : `xgt0 , x-2 gt0`
`rarr x gt 0,, xgt2`

Promotional Banner

Topper's Solved these Questions

  • 3-D GEOMETRY

    NDA PREVIOUS YEARS|Exercise MCQ|147 Videos

  • BINOMIAL THEROREM, MATHEMATICAL INDUCTION

    NDA PREVIOUS YEARS|Exercise MQS|65 Videos

Similar Questions

Explore conceptually related problems

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

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

The function f(x)=x^3-3x^2-24x+5 is an increasing function in the interval

The function f(x)=2x^(3)-15x^(2)-144x-7 is increasing for

2x^(3) - 6x + 5 is an increasing function, if

The function f(x)=x^(3)+3x is increasing on

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

NDA PREVIOUS YEARS-APPLICATION OF DERIVATIVES -Example
  1. Which one of the following statement is correct ?

    Text Solution

    |

  2. The radius of a circle is increasing uniformly at the rate of 3 cm/...

    Text Solution

    |

  3. The function f(x)=x^(3)-3x^(2)+6 is an increasing funciton for :

    Text Solution

    |

  4. What is the minimum value of |x|?

    Text Solution

    |

  5. The function f(x)=x^(2)-4x, x in [0,4] attains minimum value at

    Text Solution

    |

  6. The curve y =xe^(x) has minimum value equal to

    Text Solution

    |

  7. The maximum value of the function f(x)=x^(3)+2x^(2)-4x+6 exits at

    Text Solution

    |

  8. The minimum value of the function F(x)=|x-4| exists at

    Text Solution

    |

  9. What is the slope of the tangent to the curve y=sin^(1)(sin^(2)x)

    Text Solution

    |

  10. Consider the curve y=e^(2x) What is the slope of the tangent to the ...

    Text Solution

    |

  11. The tangent to the curve y=e^(2x) at the point (0,1) meets X-axis at

    Text Solution

    |

  12. Consider the function f(X)=(x^(2)-x+1)/(x^(2)+x+1) What is the maxim...

    Text Solution

    |

  13. Consider the function f(X)=(x^(2)-x+1)/(x^(2)+x+1) What is the minim...

    Text Solution

    |

  14. A rectangular box is to be made form a sheet of 24 inch length and 9 ...

    Text Solution

    |

  15. A rectangular box is to be made form a sheet of 24 inch length and 9 ...

    Text Solution

    |

  16. Show that the height of the cylinder of maximum volume that can be ...

    Text Solution

    |

  17. A cylinder is inscribed in a sphere of radius r What is the radius o...

    Text Solution

    |

  18. Consider the following statements 1. y=(e^(x)+e^(-x))/(2) is an incr...

    Text Solution

    |

  19. Consider the function f(X)=(x^(2)-1)/(x^(2)+1) where x in R At what ...

    Text Solution

    |

  20. What is the minimum value of f(X)?

    Text Solution

    |