Home
Class 12
MATHS
Show that f(x)=sinx-cosx is an increasin...

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

Text Solution

Verified by Experts

We have given
`f(x)=sinx-cosx`
Then we have to show, `f(x)` is increasing function on `(-pi/4,pi/4)`
`f(x)=sinx−cosx`
`f′(x)=cosx+sinx`
`f(x)=sqrt2(1/(sqrt2)cosx+1/(sqrt2)sinx)`
`f(x)=sqrt2sin(pi/4+x)`>`0 in pi/4+x in(-pi/2,pi/2)`
`-pi/2`<`pi/4+x`<`pi/2`
...
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)=sin x is an increasing function on (-pi/2,pi/2)

f(x) = e^(sinx+cosx) is an increasing function in

Show that f(x)=cos(2x+pi/4) is an increasing function on (3 pi/8,7 pi/8)

Show that f(x)=cos(2x+(pi)/(4)) is an increasing function on (3 pi/8,7 pi/8)

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

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (-(pi)/(2),(pi)/(4))(b)(0,(pi)/(2))(-(pi)/(2),(pi)/(2))(d)((pi)/(4),(pi)/(2))

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

The function f(x)=tan^(-1)(sin x+cos x) is an increasing function in (1)((pi)/(4),(pi)/(2))(2)(-(pi)/(2),(pi)/(4))(3)(0,(pi)/(2))(4)(-(pi)/(2),(pi)/(2))^(((pi)/(4)),(pi)/(2))^(((pi)/(4)))(2)

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

RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. Prove that the function f(x)=x^3-6x^2+12 x-18 is increasing on R .

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  4. Show that f(x)=tan^(-1)x-x is decreasing function on Rdot

    Text Solution

    |

  5. Determine whether f(x)=-x/2+sinx is increasing or decreasing on (-pi/3...

    Text Solution

    |

  6. Find the intervals in which f(x)=log(1+x)-x/(1+x) is increasing or dec...

    Text Solution

    |

  7. Find the intervals in which f(x)=(x+2)e^(-x) is increasing or decreasi...

    Text Solution

    |

  8. Show that the function f given by f(x)=10^x is increasing for all x .

    Text Solution

    |

  9. Prove that the function f given by f(x)=x-[x] is increasing in (0,\ 1)...

    Text Solution

    |

  10. Prove that the function f(x)=3x^5+40 x^3+240 x is increasing on R .

    Text Solution

    |

  11. Prove that the function f given by f(x)=logcosx is strictly increasing...

    Text Solution

    |

  12. Show that the function f given by f(x)=x^3-3x^2+4x ,x in Ris strictl...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

  15. Prove that the function f(x)=cosx is neither increasing nor decreas...

    Text Solution

    |

  16. Show that f(x)=x^2-xsinx is an increasing function on (0,\ pi//2) .

    Text Solution

    |

  17. Find the value(s) of a for which f(x)=x^3-a x is an increasing functio...

    Text Solution

    |

  18. Find the values of b for which the function f(x)=sinx-b x+c is a decre...

    Text Solution

    |

  19. Show that f(x)=x+cosx-a is an increasing function on R for all values ...

    Text Solution

    |

  20. Let f defined on [0, 1] be twice differentiable such that | f"(x)| ...

    Text Solution

    |