Home
Class 12
MATHS
The fucntion f(x)=x+cos x is...

The fucntion f(x)=x+cos x is

A

always increasing

B

always decreasing

C

increasing for certain range of x

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
A
Given, `f(x)=x+cosx`
On differentiating w.r.t. x, we get
`f'(x)=1-sinx`
`impliesf'(x)gt0`, for all values of x.
[`because`sinx lies between -1 and 1]
`thereforef(x)` is always increasing.
Promotional Banner

Topper's Solved these Questions

  • PRACTICE SET 03

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise PAPER 2 (MATHEMATICS)|49 Videos

  • PRACTICE SET 05

    MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS|Exercise Paper 2 (Mathematics)|50 Videos

Similar Questions

Explore conceptually related problems

The function f(x)=x+cos x is

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

For the fucntion f(x)=x cos ""1/x, x ge 1 which one of the following is incorrect ?

The fucntion f(x) =x^3-3x, is

The function f(x) = sin x + cos x will be

The fucntion f(x) =(sin x)/(x) is decreasing in the interval

At how many points is the fucntion f(x)=[x] discontinuous?

In the interval (0,pi//2) the fucntion f(x)= tan^nx+cot^n x attains

MHTCET PREVIOUS YEAR PAPERS AND PRACTICE PAPERS-PRACTICE SET 04-PAPER 2 (MATHMATICS)
  1. if the function f:R to R be defined by f(x)=tanx-x, then f(x) always

    Text Solution

    |

  2. int(0)^(pi)(xdx)/(1+sinx) is equal to

    Text Solution

    |

  3. If f(x)=x+1/x ,\ \ x >0 , then its greatest value is -2 (b) 0 (c) 3...

    Text Solution

    |

  4. The sum to infinity of the series 1+2/3+6/(3^2)+(10)/(3^3)+(14)/(3^...

    Text Solution

    |

  5. A straight line passes through the points (5,0) and (0,3). The length ...

    Text Solution

    |

  6. The ratio by which the line 2x + 5y -7=0 divides the straight line joi...

    Text Solution

    |

  7. Let A (2,-3) and B(-2,1) be vertices of a triangle ABC. If the centroi...

    Text Solution

    |

  8. A hyperbola passes through a focus of the ellipse x^2/169 + y^2/25=1. ...

    Text Solution

    |

  9. If A=[(1,-2,1),(2,1,3)] and B=[(2,1),(3,2),(1,1)] then (AB)' is equal ...

    Text Solution

    |

  10. If equation 4x^(2)+2pxy+25y^(2)+2x+5y-1=0 represents parallel lines,...

    Text Solution

    |

  11. A bag contains 5 brown and 4 white socks. A man pulls out two socks. ...

    Text Solution

    |

  12. The fucntion f(x)=x+cos x is

    Text Solution

    |

  13. The logically equivalent proposition of p iff q is

    Text Solution

    |

  14. If vec u ,"" vec v , vec w are noncoplanar vectors and p, q are re...

    Text Solution

    |

  15. int(-1)^(0)(dx)/(x^(2)+2x+2) is equal to

    Text Solution

    |

  16. A particle moves along the curve y=x^2+2xdot At what point(s) on the c...

    Text Solution

    |

  17. If alpha=x(a xxb)+y(b xxc)+z(cxxa) and [abc]=(1)/(8), then x+y+z is eq...

    Text Solution

    |

  18. The angle between the lines x=1, y=2 and y=-1, z=0 is

    Text Solution

    |

  19. If the range ot a random vaniabie X is 0,1,2,3, at P(X=K)=((K+1)/3^k) ...

    Text Solution

    |

  20. An anti-aircraft gun can take a maximum of four shots at an enemy plan...

    Text Solution

    |