Home
Class 12
MATHS
Show that f(x)=(log)a x ,\ \ 0<a<1 is a ...

Show that `f(x)=(log)_a x ,\ \ 00` .

Text Solution

Verified by Experts

`f(x)=log _a ​ (x)` `0`f ′ (x)= ...
Promotional Banner

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos

Similar Questions

Explore conceptually related problems

Show that f(x)=(log x)/(x), x ne 0 is maximum at x = e .

Show that f(x)=log sin x is increasing on (0,pi/2) and decreasing on (pi/2,pi).

The function f(x)=log x

Show that f(x)=(x)/(sqrt(1+x))- ln (1+x) is an increasing function for x gt -1 .

The function f(x)=x log x

Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) is increasing in R

Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) is increasing on R.

If f(x)=x ln x-2, then show that f(x)=0 has exactly one root in the interval (1,e).

RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Show that f(x)=e^(2x) is increasing on R .

    Text Solution

    |

  2. Show that f(x)=e^(1//x),\ \ x!=0 is a decreasing function for all x...

    Text Solution

    |

  3. Show that f(x)=(log)a x ,\ \ 0<a<1 is a decreasing function for all ...

    Text Solution

    |

  4. Show that f(x)=sinx is increasing on (0,\ pi//2) and decreasing on (pi...

    Text Solution

    |

  5. Show that f(x)=logsinx is increasing on (0,\ pi//2) and decreasing on ...

    Text Solution

    |

  6. Show that f(x)=x-sinx is increasing for all x in R .

    Text Solution

    |

  7. Show that f(x)=x^3-15 x^2+75 x-50 is an increasing function for all...

    Text Solution

    |

  8. Show that f(x)=cos^2x is a decreasing function on (0,\ pi//2) .

    Text Solution

    |

  9. Show that f(x)=sinx is an increasing function on (-pi//2,\ pi//2) .

    Text Solution

    |

  10. Show that f(x)=cosx is a decreasing function on (0,\ pi) , increasing ...

    Text Solution

    |

  11. Show that f(x)=tanx is an increasing function on (-pi//2,\ pi//2) .

    Text Solution

    |

  12. Show that f(x)=tan^(-1)(sinx+cosx) is a decreasing function on the ...

    Text Solution

    |

  13. Show that the function f(x)=sin(2x+pi//4) is decreasing on (3pi//8,\ 5...

    Text Solution

    |

  14. Show that the function f(x)=cot^(-1)(sinx+cosx) is decreasing on (0,\ ...

    Text Solution

    |

  15. Show that f(x)=(x-1)e^x+1 is an increasing function for all x >0 .

    Text Solution

    |

  16. Show that the function x^2-x+1 is neither increasing nor decreasing...

    Text Solution

    |

  17. Show that f(x)=x^9+4x^7+11 is an increasing function for all x in ...

    Text Solution

    |

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

    Text Solution

    |

  19. State when a function f(x) is said to be increasing on an interval ...

    Text Solution

    |

  20. Show that f(x)=sinx-cosx is an increasing function on (-pi//4,\ pi//4)...

    Text Solution

    |