Home
Class 12
MATHS
Wht is the interval over which the funct...

Wht is the interval over which the function `f(x)=6x-x^(2),x gt 0` is increasing ?

A

(0,3)

B

(3,6)

C

(6,9)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given f(x)=`6x^(2)-x^(2), x gt 0`
Differentiate w.r.t x both side we get
f(x)=6-2x
As we know f(X) will be increasing funciton if
`f(X) gt0 therefore 6-2x gt 0 rarr x lt 3`
Thus required interval is (0,3)
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

What is the interval in which the function f(x) = sqrt(9-x^(2)) is increasing ? (f(x)gt0)

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

The interval in which the function f(x)=2x^(3)-9x^(2)+12x-15 is increasing, is :

Find the intervals in which the function f(x)=x^(3)-12x^(2)+36x+117 is increasing

The interval on which the function f(x)=2x^(2)-3x is increasing or decreasing in :

The function f(x)=x^(2)-6x+9 is increasing for x gt3.

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

NDA PREVIOUS YEARS-APPLICATION OF DERIVATIVES -Example
  1. Statement I : y= -tan^(-1)(x^(-1))+1 is an increasing function of x S...

    Text Solution

    |

  2. least value of the function f(x)=2x^3-3x^2-12x+1 on [-2,2.5]

    Text Solution

    |

  3. Wht is the interval over which the function f(x)=6x-x^(2),x gt 0 is in...

    Text Solution

    |

  4. If f and g are two decreasing function such that fog is defined, then ...

    Text Solution

    |

  5. For a point of inflection of y= f(X) which one of the following is cor...

    Text Solution

    |

  6. What is the value of p for which the funtion f(X)=p sinx+(sin 3x)/(3...

    Text Solution

    |

  7. If at any instant t for a sphere r denotes the radius s denotes the su...

    Text Solution

    |

  8. The function f(X)=k sinx +1/3 sinx 3x has maximum value at x=(pi)/(3) ...

    Text Solution

    |

  9. Consider the following statement in respect of the function f(x)=x^(...

    Text Solution

    |

  10. The largest value of 2x^(3)-3x^(2)-12x+5 for -2 le x le 2 occurs when

    Text Solution

    |

  11. The function y=f(x)=mx+c has

    Text Solution

    |

  12. At an extreme point of a function f(X) the tangent to the curve is

    Text Solution

    |

  13. The point in the interval [0,2pi] where f(x) =e^(x) sinx has maximum s...

    Text Solution

    |

  14. If the rate of change in volume of spherical soap bubble is uniform th...

    Text Solution

    |

  15. If f(X)=x ln x then f(x) attains minumum value at which one of the fol...

    Text Solution

    |

  16. Find the points on the curve x^2+y^2-2x-3=0at which the tangents are ...

    Text Solution

    |

  17. Which of the following statement is correct ?

    Text Solution

    |

  18. How many tangents are parallel to X-axis for the curve y = x^2 - 4x + ...

    Text Solution

    |

  19. What is the rate of change of sqrt(x^(2)+16) with respect to x^(2) at ...

    Text Solution

    |

  20. The slope of the tangent to the curve x=t^2+3t-8,y=2t^2-2t-5at the po...

    Text Solution

    |