Home
Class 12
MATHS
f(x)=2x-tan^(-1)x-log|x+sqrt(1+x^(2))| i...

`f(x)=2x-tan^(-1)x-log|x+sqrt(1+x^(2))|` is ……….. `(x in R)`

A

increasing on R

B

decreasing on R

C

has a minimum at x = 1

D

has a maximum at x = 1

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK|51 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise SOLUTIONS OF NCERT EXEMPLAR PROBLEMS (SHORT ANSWER TYPE QUESTIONS)|24 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise PRACTICE WORK|85 Videos

  • ANNUAL EXAMINATION :SAMPLE PAPER

    KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos

  • APPLICATION OF INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

f(x)=2x+cot^(-1)x-log|x + sqrt(1+x^(2))| is …………..

Show that f(x)=2x+cot^(-1)x+log(sqrt(1+x^(2))-x) is increasing in R.

Let f(x)= sqrt(1+x^(2)) then,

f(x)=int(2-(1)/(1+x^(2))-(1)/(sqrt(1+x^(2))))dx then f is …………

int(log|x|)/(x sqrt(1+log|x|))dx=...+c .

F(x)=x^(5)+log,(x+sqrt(1+x^(2))) , Then for all alpha, beta in R such that alpha+beta gt 0

Prove that, (d)/(dx) ["log" (x^(2) + x + 1)/(x^(2) -x + 1) + (2)/(sqrt3) "tan"^(-1) (sqrt3x)/(1-x^(2))]= (4)/(x^(4 ) + x^(2) + 1)

Differentiate tan^(-1) ((sqrt(1+x^(2))-1)/(x)) w.r.t tan^(-1)x , where x ne 0

f(x)=sin^(-1){sqrt3/2x-1/2sqrt(1-x^(2))},-1/2lexle1 then f(x) = _____

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -TEXTBOOK BASED MCQS
  1. Find the points on the curve x^(2)+y^(2)-2x-3=0 at which the tangents ...

    Text Solution

    |

  2. The point on y^(2)=x where tangent makes angle of measure (pi)/(4) wit...

    Text Solution

    |

  3. A cone with its height equal to the diameter of the base is expanding ...

    Text Solution

    |

  4. The rate of increase of f(x)=x^(3)-5x^(2)+5x+25 is twice the rate of i...

    Text Solution

    |

  5. The radius of the cone is increasing at the rate of 4 cm/se. Its heigh...

    Text Solution

    |

  6. The rate of change of surface area of a sphere w.r.t. radius is ………..

    Text Solution

    |

  7. The rate of change of volume of a cylinder w.r.t. radius whose radius ...

    Text Solution

    |

  8. f(x)=tan^(-1)x-x, is …………

    Text Solution

    |

  9. f(x)=2x-tan^(-1)x-log|x+sqrt(1+x^(2))| is ……….. (x in R)

    Text Solution

    |

  10. If ……….., then f(x)=x^(2)-kx+20, [0,3] is strictly increasing.

    Text Solution

    |

  11. f(x)=|x-1|+|x-2| is increasing if ………..

    Text Solution

    |

  12. The points on the curve 9y^(2)=x^(3), where the normal to the curve ma...

    Text Solution

    |

  13. y=mx+4 touches y^(2)=8x, if m = ………..

    Text Solution

    |

  14. The measure of the angle between the curves y=2 sin^(2)x and y = cos 2...

    Text Solution

    |

  15. The normal to x^(2)=4y passing through (1, 2) has equation ……….

    Text Solution

    |

  16. The local minimum value of x^(2)+(16)/(x)(x ne 0) is ………….

    Text Solution

    |

  17. The minimum value of sec x, x in [(2pi)/(3),pi] is ……….

    Text Solution

    |

  18. The maximum value of cosec x, x in [(pi)/(6), (pi)/(3)] is ………

    Text Solution

    |

  19. (31)^((1)/(5)) has approximate value ………..

    Text Solution

    |

  20. f(x)=x^(2)+4x+5 has minimum value ………… (x in R)

    Text Solution

    |