Home
Class 12
MATHS
If f"(x) > 0 and f(1) = 0 such that g(x)...

If f"(x) > 0 and f(1) = 0 such that `g(x) = f(cot^2x + 2cotx + 2) where 0 < x < pi`, then g'(x) decreasing in (a, b). where `a + b + pi/4`…

A

`(0,pi)`

B

`((pi)/(2),pi)`

C

`((3pi)/(4),pi)`

D

`(0,(3pi)/(4))`

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise EXAMPLE|23 Videos
  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|7 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

If f''(x) = sec^(2) x and f (0) = f '(0) = 0 then:

If f(x) is a continuous function in [0,pi] such that f(0)=f(x)=0, then the value of int_(0)^(pi//2) {f(2x)-f''(2x)}sin x cos x dx is equal to

STATEMENT - 1 : Let f be a twice differentiable function such that f'(x) = g(x) and f''(x) = - f (x) . If h'(x) = [f(x)]^(2) + [g (x)]^(2) , h(1) = 8 and h (0) =2 Rightarrow h(2) =14 and STATEMENT - 2 : h''(x)=0

If f(x) and g(x) are differentiable function for 0 le x le 23 such that f(0) =2, g(0) =0 ,f(23) =22 g (23) =10. Then show that f'(x)=2g'(x) for at least one x in the interval (0,23)

Let f_(1) (x) and f_(2) (x) be twice differentiable functions where F(x)= f_(1) (x) + f_(2) (x) and G(x) = f_(1)(x) - f_(2)(x), AA x in R, f_(1) (0) = 2 and f_(2)(0)=1. "If" f'_(1)(x) = f_(2) (x) and f'_(2) (x) = f_(1) (x) , AA x in R then the number of solutions of the equation (F(x))^(2) =(9x^(4))/(G(x)) is...... .

Let f :R to R be a continous and differentiable function such that f (x+y ) =f (x). F(y)AA x, y, f(x) ne 0 and f (0 )=1 and f '(0) =2. Let g (xy) =g (x). g (y) AA x, y and g'(1)=2.g (1) ne =0 The number of values of x, where f (x) g(x):

If f"(x)>0AAx in R, f'(3)=0,and g(x)=f("tan"hat2x-2"tan"x+4),0

Let f(x) be a continuous function for all x in R and f'(0) =1 then g(x) = f(|x|)-sqrt((1-cos 2x)/(2)), at x=0,

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

If f(x), g(x) be twice differentiable functions on [0,2] satisfying f''(x) = g''(x) , f'(1) = 2g'(1) = 4 and f(2) = 3 g(2) = 9 , then f(x)-g(x) at x = 4 equals (A) 0 (B) 10 (C) 8 (D) 2

ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
  1. If f"(x) > 0 and f(1) = 0 such that g(x) = f(cot^2x + 2cotx + 2) where...

    Text Solution

    |

  2. The least value of alpha in R for which 4ax^2+(1)/(x)ge1, for all xgt ...

    Text Solution

    |

  3. The number of points in (-oo,oo), for which x^2-xsinx-cosx=0, is

    Text Solution

    |

  4. Let f : R ->(0,oo) and g : R -> R be twice differentiable functions...

    Text Solution

    |

  5. Let f:(0,oo)vecR be given by f(x)=int(1/x)^x(e^(-(t+1/t))dt)/t , then ...

    Text Solution

    |

  6. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|| has a local minimum or a loca...

    Text Solution

    |

  7. A rectangular sheet of fixed perimeter with sides having their lengths...

    Text Solution

    |

  8. A vertical line passing through the point (h, 0) intersects the ellips...

    Text Solution

    |

  9. Let f,g and h be real-valued functions defined on the interval [0,1] b...

    Text Solution

    |

  10. e total number of local maxima and local minima of the function f(x) =...

    Text Solution

    |

  11. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

    Text Solution

    |

  12. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

    Text Solution

    |

  13. If f(x)=x^3+bx^2+cx+d and 0<b^2<c, then

    Text Solution

    |

  14. If f(x)=x^2+2b x+2c^2 and g(x)= -x^2-2c x+b^2 are such that min f(x...

    Text Solution

    |

  15. The length of the longest interval in which the function 3sinx-4sin^3x...

    Text Solution

    |

  16. If f(x)=e^(1-x) then f(x) is

    Text Solution

    |

  17. The maximum value of (cosalpha(1))(cos alpha(2))...(cosalpha(n)), un...

    Text Solution

    |

  18. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

    Text Solution

    |

  19. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

    Text Solution

    |

  20. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

    Text Solution

    |

  21. about to only mathematics

    Text Solution

    |