Home
Class 12
MATHS
f(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+...

`f(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)`

A

a) `f(x)` is increasing for all `x in R`

B

b) `f(x)` is decreasing for all `x in R`

C

c) `f(x)` is increasing in its domain

D

d) none of the above

Text Solution

Verified by Experts

The correct Answer is:
C
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|16 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|8 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 5|8 Videos

  • MATRICES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|49 Videos

  • PAIR OF STRAIGHT LINES

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|2 Videos

Similar Questions

Explore conceptually related problems

tan 5x tan3x tan2x=

f(x)=4tanx-tan^2x+tan^3x ,x!=npi+pi/2, (a)is monotonically increasing (b)is monotonically decreasing (c)has a point of maxima (d)has a point of minima

Prove that tan (2 tan^(-1) x ) = 2 tan (tan^(-1) x + tan^(-1) x^(3)) .

If f'(x) = tan^(-1)(Sec x + tan x), x in (-pi/2 , pi/2) and f(0) = 0 then the value of f(1) is

Consider the function f(x)=(sin 2x)^(tan^(2)2x), x in (pi)/(4) . The value of f((pi)/(4)) such that f is continuous at x=(pi)/(4) is

Let f : I - {-1,0,1} to [-pi, pi] be defined as f(x) = 2 tan^(-1) x - tan^(-1)((2x)/(1 -x^(2))) , then which of the following statements (s) is (are) correct ?

If tan ^(-1) 2x + tan ^(-1) 3 xx = (pi)/(4) , then x = ?

tan 8x = (2 tan 4x)/(1 - tan ^(2) 4x)

Solve tan^(-1)2x+tan^(-1)3x=pi/4 .

Solve : tan^(-1)2x+tan^(-1)3x=pi/4

ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-Exercise (Single Option Correct Type Questions)
  1. sinx+cosx=y^2-y+a has no value of x for any value of y if a belongs to...

    Text Solution

    |

  2. f: R->R is defined by f(x)=(e^(x^2)-e^(-x^2))/(e^(x^2)+e^(-x^2)) is :

    Text Solution

    |

  3. Suppose that f(x) is a quadratic expresson positive for all real xdot ...

    Text Solution

    |

  4. Let f(x)=min{1,cos x,1-sinx}, -pi le x le pi, Then, f(x) is

    Text Solution

    |

  5. f(x)={2-|x^2+5x+6|,x!=2a^2+1,x=-2T h e nt h er a ngeofa , so that f(x...

    Text Solution

    |

  6. Maximum number of real solution for the equation ax^(n)+x^(2)+bx+c=0...

    Text Solution

    |

  7. Maximum number area of rectangle whose two sides are x=x(0),x=pi-x(0...

    Text Solution

    |

  8. f(x)=-1+kx+k neither touches nor intecepts the curve f(x)= Iog x, then...

    Text Solution

    |

  9. f(x) is polynomial of degree 4 with real coefficients such that f(x)=0...

    Text Solution

    |

  10. A curve whose concavity is directly proportional to the logarithm of i...

    Text Solution

    |

  11. f(x) = 4 tan x-tan^(2)x+tan^(3)x,xnenpi+(pi)/(2)

    Text Solution

    |

  12. f (x)= {{:(3+|x-k|"," , x le k),(a ^(2) -2 + ( sin (x -k))/((x-k))"," ...

    Text Solution

    |

  13. Let f(x) be linear functions with the properties that f(1) le f(2), f(...

    Text Solution

    |

  14. If P(x) is polynomial satisfying P(x^(2))=x^(2)P(x)andP(0)=-2, P'(3//2...

    Text Solution

    |

  15. Find the vertex and length of latus rectum of the parabola x^(2)=-4(y-...

    Text Solution

    |

  16. Let f(x)=x^(2)-2xandg(x)=f(f(x)-1)+f(5-f(x)), then

    Text Solution

    |

  17. Let f:NrarrN in such that f(n+1)gtf(f(n)) for all n in N then

    Text Solution

    |

  18. The equation |2ax-3|+|ax+1|+|5-ax|=(1)/(2) possesses

    Text Solution

    |

  19. Let a(1),a(2),a(n) be sequence of real numbers with a(n+1)=a(n)+sqrt(1...

    Text Solution

    |

  20. A function f is defined by f(x)=|x|^m|x-1|^nAAx in Rdot The local max...

    Text Solution

    |