Home
Class 12
MATHS
Show that the function f(x) = x -sin x i...

Show that the function f(x) = x -sin x is an increasing function `forall x in R`.

Text Solution

Verified by Experts

f(x) = x - sin x
`rArr" "f'(x) =1 - cos x`
We know that
`-1 le cos x le 1 " "forall x in R`
`rArr -1le - cos x le 1`
`rArr 0 le1 - cos x le 2 `
`rArr 0 lef' (x) le 2`
`rArr` The value of f'(x) is a zero or greater than zero.
Therfore f (x) = x - sin x in increasing function on R.
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6a|20 Videos

  • APPLICATIONS OF DERIVATIVES

    NAGEEN PRAKASHAN|Exercise Exercise 6b|11 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Show that the function f(x) = 5x - 2 is a strictly increasing function on R

The function f(x) = sin|x| is

Show that the function f(x) = 3x + 2 is strictly increasing function on R.

Show that the function f(x)= x^(3) - 3x^(2)+3x - 1 is an increasing function on R.

Prove that f(x)=x-sin x is an increasing function.

Show that the function f(x)=2x+3 is strictly increasing function on R.

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

Without using the derivative show that the function f(x)=7x-3 is strictly increasing function on R.

Without using the derivative show that the function f(x)=7x-3 is strictly increasing function on R.

Is the function f(x)=x^(2), x in R increasing?

NAGEEN PRAKASHAN-APPLICATIONS OF DERIVATIVES-Miscellaneous Exercise
  1. Show that the function f(x) = x -sin x is an increasing function foral...

    Text Solution

    |

  2. Using differentials, find the approximate value of each of the follow...

    Text Solution

    |

  3. Show that the function given by f(x)=(logx)/xhas maximum at x = e.

    Text Solution

    |

  4. The two equal sides of an isosceles triangle with fixed base b are ...

    Text Solution

    |

  5. Find the equation of the normal to the curve x^2=4ywhich passes throu...

    Text Solution

    |

  6. Show that the normal at any point theta to the curve x=acostheta+at...

    Text Solution

    |

  7. Find the intervals in which the function f given by f(x)=(4sinx-2x-x c...

    Text Solution

    |

  8. Find the intervals in which the function f given by f(x)=\ x^3+1/(...

    Text Solution

    |

  9. Find the maximum area of an isosceles triangle inscribed in the ellip...

    Text Solution

    |

  10. A tank with rectangular base and rectangular sides, open at the top is...

    Text Solution

    |

  11. The sum of the perimeter of a circle and square is k, where k is so...

    Text Solution

    |

  12. A window is in the form of a rectangle surmounted by a semicircular...

    Text Solution

    |

  13. A point on the hypotenuse of a triangle is at distance a and b from t...

    Text Solution

    |

  14. Find the points at which the function f given by f(x)=(x-2)^4(x+1)^3 h...

    Text Solution

    |

  15. Find the absolute maximum and minimum values of the function f give...

    Text Solution

    |

  16. Show that the altitude of the right circular cone of maximum volume...

    Text Solution

    |

  17. Let f be a function defined on [a, b] such that f^(prime)(x)>0, for al...

    Text Solution

    |

  18. Show that the height of the cylinder of maximum volume that can be in...

    Text Solution

    |

  19. Show that height of the cylinder of greatest volume which can be insc...

    Text Solution

    |

  20. A cylindrical tank of radius 10 m is being filled with wheat at the r...

    Text Solution

    |

  21. The slope of the tangent to the curve x=t^2+3t-8,y=2t^2-2t-5at the po...

    Text Solution

    |