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

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

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6c|19 Videos
  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6d|24 Videos
  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercise 6a|20 Videos
  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Show that the function f(x) = log cos x is : (i) Strictly decreasing in ]0,pi/2[ (ii) Strictly increasing in ]pi/2, pi [

Prove that the function f given by f(x)=logcosx is strictly increasing on (-pi//2,\ 0) and strictly decreasing on (0,\ pi//2) .

Prove that the function f(x)=cosx is strictly decreasing in (0,\ pi)

Prove that the function f given by f(x) = log | cos x|" is decreasing on "(0,pi/2)" and increasing on "((3pi)/2,2pi) .

Prove that the function f(x)=cosx is strictly increasing in (pi,\ 2pi)

Prove that the function f(x)=cosx is neither increasing nor decreasing in (0,\ 2pi)

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

Show that f(x)=cosx is a decreasing function on (0,\ pi) , increasing in (pi,\ 0) and neither increasing nor decreasing in (pi,\ pi) .

Show that f(x)=cosx is decreasing function on (0,pi), increasing in (-pi,0) and neither increasing nor decreasing in (-pi,pi)dot

Prove that the function f(x)=tanx-4x is strictly decreasing on (-pi//3,\ pi//3) .

NAGEEN PRAKASHAN ENGLISH-APPLICATIONS OF DERIVATIVES-Exercise 6b
  1. Show that the function f(x) = 3x + 2 is strictly increasing function o...

    Text Solution

    |

  2. Show that the function f(x)= x^(2)is strictly increasing function in t...

    Text Solution

    |

  3. Show that the function f(x) = (x - 1) e^(x)+2 is strictly increasing f...

    Text Solution

    |

  4. Show that the function f(x)=a^x ,\ a >1 is strictly increasing on Rdot

    Text Solution

    |

  5. Show that the function f(x) =- 5x + 2 is strictly decreasing function ...

    Text Solution

    |

  6. Prove that the function given by f(x) = cos xis(a) strictly decreasing...

    Text Solution

    |

  7. Find the intervals in which the following functions are: (i) increas...

    Text Solution

    |

  8. Show that the function f(x) = 1/(1+x^(2)) is increasing function in th...

    Text Solution

    |

  9. Show that the function f(x)=x^(3)+1/(x^(3)) is decreasing function in ...

    Text Solution

    |

  10. Show that y='log(1+x)-(2x)/(2+x)', is an increasing function of x thro...

    Text Solution

    |

  11. Find the intervals in which the function f(x)=log(1+x)-(2x)/(2+x) is i...

    Text Solution

    |

  12. Let I be an interval disjointed from [-1,\ 1] . Prove that the functio...

    Text Solution

    |

  13. Show that the function f(x) = log (sin x) (i) is strictly increasing...

    Text Solution

    |

  14. Show that the function f(x)=sin^(4) x+ cos^(4) x (i) is decreasing i...

    Text Solution

    |

  15. Find the intervals in which the function f given f(x)=\ s in x+cosx ,\...

    Text Solution

    |

  16. Show that the function f(x) = log cos x is : (i) Strictly decreasin...

    Text Solution

    |

  17. prove that (x)/(1+x) lt log (1+x)ltx, for all xgt 0

    Text Solution

    |