Home
Class 12
MATHS
Show that the function f(x)=sin^(4) x+ c...

Show that the function `f(x)=sin^(4) x+ cos^(4) x`
(i) is decreasing in the interval`[0,pi/4]`.
(ii) is increasing in the interval `[pi/4,pi/2]`.

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 (sin x) (i) is strictly increasing in the interval ]0,pi/2[ . (ii) is strictly decreasing in the interval ]pi/2,pi[ .

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

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

The function f(x)=sin^4x+cos^4x increasing in interval

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

f(x) = sin^(4)x+cos^(4)x in [0,(pi)/(2)]

Show that f(x)=tan^(-1)(sinx+cosx) is decreasing function on the interval (pi/4,pi/2)dot

Show that f(x)=tan^(-1)(sinx+cosx) is a decreasing function on the interval on (pi//4,\ pi//2) .

Show that f(x)=tan^(-1)(sinx+cosx) is an increasing function on the interval (0,\ pi//4) .

Show that the function f(x)=cot^(-1)(sinx+cosx) is decreasing on (0,\ pi//4) and increasing on (pi//4,\ pi//2) .

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

    |