Home
Class 12
MATHS
Prove that the function f given by f (x)...

Prove that the function f given by f (x) = log(sin x) is strictly increasing on `(0,pi/2)` strictly decreasing on `(pi/2 , pi)`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT TELUGU|Exercise EXERCISE 6.3|31 Videos

  • APPLICATION OF DERIVATIVES

    NCERT TELUGU|Exercise EXERCISE 6.4|23 Videos

  • APPLICATION OF DERIVATIVES

    NCERT TELUGU|Exercise EXERCISE 6.1|18 Videos

  • APPLICATION OF INTEGRALS

    NCERT TELUGU|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Prove that the function log sin x is strictly increasing (0,pi/2) and strictly decreasing on (pi/2,pi)

Prove that the function f given by f(x) = x ^(2) – x + 1 is neither strictly increasing nor decreasing on (– 1, 1).

Show that f(x) = cos^(2) x is strictly decreasing on (0, pi//2) .

Prove that the function given by f(x) = cos x is (a) decreasing in (0, pi ) (b) increasing in (pi, 2pi) , and (c) neither increasing nor decreasing in (0, 2pi) .

Show that f(x)=|x| is strictly decreasing on (-oo, 0) and strictly increasing on (0, oo) .

Show that the function f given by f(x) = tan^(-1)(sin x + cos x), x gt 0 is always an strictly increasing functions in (0, (pi)/(4))

Define the strictly increasing function and strictly decreasing function on an interval.

Show that the function f(x) = sin x defined on R is neither increasing nor decreasing on (0, pi) .

Give an example of a trigonometric function which is Strictly increasing on (0,pi/2)

Find the intervals in which the following functions are strictly increasing or strictly decreasing. x e^(x)

NCERT TELUGU-APPLICATION OF DERIVATIVES-EXERCISE 6.2
  1. Find the intervals in which the function f given by f(x) = 2x^(2) – 3x...

    Text Solution

    |

  2. Find the intervals in which the function f given by f(x) = 2x^(3) – 3x...

    Text Solution

    |

  3. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  4. Find the intervals in which the functions are strictly increasing or ...

    Text Solution

    |

  5. Find the intervals in which the functions are strictly increasing or ...

    Text Solution

    |

  6. Find the intervals in which the following functions are strictly incre...

    Text Solution

    |

  7. Find the intervals in which the functions are strictly increasing or ...

    Text Solution

    |

  8. If f(x)=log (1+x)-(2x)/(2+x) is increasing , then………..

    Text Solution

    |

  9. Find the values of x for which y = [x(x – 2)]^(2) is an increasing fu...

    Text Solution

    |

  10. Prove that y = 4sin theta/(2 + cos theta) - theta, is an increasing fu...

    Text Solution

    |

  11. Prove that the logarithmic function is increasing on (0, oo).

    Text Solution

    |

  12. Prove that the function f given by f(x) = x ^(2) – x + 1 is neither st...

    Text Solution

    |

  13. Which of the following functions are decreasing on 0,(pi)/(2) ?

    Text Solution

    |

  14. On which the following intervals in the function x^(100)+sinx-1 decre...

    Text Solution

    |

  15. For what values of a the function f given by f(x) = x^2 +ax + 1 is inc...

    Text Solution

    |

  16. Let I be any interval disjoint from [-1,1] Prove that the function f g...

    Text Solution

    |

  17. Prove that the function f given by f (x) = log(sin x) is strictly incr...

    Text Solution

    |

  18. Prove that the function f given by f(x) = log |cosx| is decreasing on ...

    Text Solution

    |

  19. Prove that the function given by f(x) = x^(3) – 3x^(2) + 3x – 100 is i...

    Text Solution

    |

  20. The interval in which y = x^(2) e^(–x) is increasing is

    Text Solution

    |