Home
Class 12
MATHS
If a function f(x) increases in the inte...

If a function `f(x)` increases in the interval `(a, b).` then the function `phi(x) = [f(x)]^n` increases in the same interval and `phi(x) != f(x)` if

A

`n=-1`

B

`n=0`

C

`n=3 `

D

`n=4 `

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise Assignment SECTION-C( Objective Type Questions ( More than one option are correct ))|1 Videos

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise Assignment SECTION-C( Objective Type Questions ( More than one option is correct ))|5 Videos

  • APPLICATION OF DERIVATIVES

    AAKASH INSTITUTE|Exercise Assignment SECTION-A (Competition Level Questions)|50 Videos

  • APPLICATION OF INTEGRALS

    AAKASH INSTITUTE|Exercise Assignment Section - I Aakash Challengers Questions|2 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=cos^(-1)x+x increases in the interval

The function f(x) = (x)/(log x) increases on the interval

The function f(x)=2log(x-2)-x^(2)+4x+1 increases in the interval

The function f(x) = x^2 is increasing in the interval

The function f(x)= tan^(-1)x +x increases in the interval

The function f(x)=x/(xlogx) increase on the interval

the function f(x)=(log x)/(x) is increasing in the interval

AAKASH INSTITUTE-APPLICATION OF DERIVATIVES-Assignment SECTION-B( Objective Type Questions ( One option is correct ))
  1. The point(s) on the curve y^3+\ 3x^2=12 y where the tangent is v...

    Text Solution

    |

  2. If f(x)=x^3+4x^2+lambdax+1 is a monotonically decreasing function of x...

    Text Solution

    |

  3. If a function f(x) increases in the interval (a, b). then the function...

    Text Solution

    |

  4. The function f, defined by f(x)=(x^(2))/(2) +In x - 2 cos x increas...

    Text Solution

    |

  5. f(x) =xe^(x(1-x)), then f(x) is

    Text Solution

    |

  6. Which of the following is correct ?

    Text Solution

    |

  7. Find the value of a , if the equation x-sinx=a has a unique r...

    Text Solution

    |

  8. Number of real roots of the equation e^(x-1)-x=0 is

    Text Solution

    |

  9. f(x)=(x)/(sinx ) and g(x)=(x)/(tanx) , where 0 lt x le 1 then in the...

    Text Solution

    |

  10. If f(x)=(p^2-1)/(p^2+1) x^3-3x + log 2 is a decreasing function of x.i...

    Text Solution

    |

  11. Let f(x) = (x-p)^2+ (x -q)^2 + (x - r)^2. Then f(x) has a minimum at ...

    Text Solution

    |

  12. The maximum value of ((1)/(x))^(2x^(2)) is

    Text Solution

    |

  13. If f(x)=alog|x|+b x^2+x has its extremum values at x=-1a n dx=2, then ...

    Text Solution

    |

  14. If x in [-1,1] then the minimum value of f(x)=x^(2)+x+1 is

    Text Solution

    |

  15. If ax+(b)/(x) ge c, AA a gt 0 and a,b,c are positive constant then

    Text Solution

    |

  16. Let x be a number which exceeds its square by the greatest possible qu...

    Text Solution

    |

  17. The point (0,3) is nearest to the curve x^(2)=2y at

    Text Solution

    |

  18. Let f(x) be a function defined as below : f(x)=sin(x^(2)-3x) ,x le...

    Text Solution

    |

  19. If lambda, mu be real numbers such that x^3-lambda x^2 + mux-6=0 has i...

    Text Solution

    |

  20. The value of c in Lagrange's mean value theorem for the function f(x) ...

    Text Solution

    |