Home
Class 12
MATHS
Consider f, g and h be three real valued...

Consider f, g and h be three real valued function defined on R. Let `f(x)=sin3x+cosx,g(x)=cos3x+sinx` and `h(x)=f^(2)(x)+g^(2)(x).` Then,
The length of a longest interval in which the function h(x) is increasing, is

A

`pi//8`

B

`pi//4`

C

`pi//6`

D

`pi//2`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise MAXIMA AND MINIMA EXERCISE 4|3 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise MAXIMA AND MINIMA EXERCISE 5|4 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS|Exercise Exercise (Statement I And Ii Type Questions)|9 Videos

  • MATRICES

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

  • PAIR OF STRAIGHT LINES

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

Similar Questions

Explore conceptually related problems

Consider f, g and h be three real valued function defined on R. Let f(x)= sin 3x + cos x , g(x)= cos 3x + sin x and h(x) = f^(2)(x) + g^(2)(x) Q. General solution of the equation h(x) = 4 , is : [where n in I ]

Suppose f, g, and h be three real valued function defined on R. Let f(x) = 2x + |x|, g(x) = (1)/(3)(2x-|x|) and h(x) = f(g(x)) The domain of definition of the function l (x) = sin^(-1) ( f(x) - g (x) ) is equal to

Suppose f, g and h be three real valued function defined on R Let f(x) =2x+|x| g(x) =1/3(2x-|x|) h(x) =f(g(x)) The range of the function k(x) = 1 + 1/pi(cos^(-1)h(x) + cot^(-1)(h(x))) is equal to

Find the interval of increase of the function f(x) = 3x + cos x

Consider f,g and h be three real valued differentiable functions defined on R. Let g(x)=x^(3)+g''(1)x^(2)+(3g'(1)-g''(1)-1)x+3g'(1) f(x)=xg(x)-12x+1 and f(x)=(h(x))^(2), where g(0)=1 Which one of the following does not hold good for y=h(x)

Consider f,g and h be three real valued functions defined on R. Let f(x)={:{(-1", "xlt0),(0", "x=0","g(x)(1-x^(2))andh(x) "be such that"),(1", "xgto):} h''(x)=6x-4. Also, h(x) has local minimum value 5 at x=1 The equation of tangent at m(2,7) to the curve y=h(x), is

Consider the real -valued function satisfyinig 2f(sinx)+f(cosx)=x. Then the domain of f(x) is

Let f be a real - valued function defined on R ( the set of real numbers) such that f(x) = sin^(-1) ( sin x) + cos^(-1) ( cos x) Number of values of x in interval (0, 3) so that f(x) is an integer, is equal to

Let f be a real - valued function defined on R ( the set of real numbers) such that f(x) = sin^(-1) ( sin x) + cos^(-1) ( cos x) The value of f(10) is equal to

Find the intervals in which the function f given by f(x) = (4 sinx-2x-x cosx)/(2+cosx) is increasing.

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Passage Based Questions)
  1. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

    Text Solution

    |

  2. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

    Text Solution

    |

  3. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

    Text Solution

    |

  4. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

    Text Solution

    |

  5. f: D->R, f(x) = (x^2 +bx+c)/(x^2+b1 x+c1) wherealpha,beta are the root...

    Text Solution

    |

  6. consider the function f(x)=(x^(2))/(x^(2)-1) The interval in which f...

    Text Solution

    |

  7. consider the function f(x)=(x^(2))/(x^(2)-1) If f is defined from R-...

    Text Solution

    |

  8. Find the value of (2! × 6! × 3!)/(3! × 5!)

    Text Solution

    |

  9. Let f(x)=e^((P+1)x)-e^(x) for real number Pgt0, then The value of x=...

    Text Solution

    |

  10. Compute 2 × 6! - 3 × 5!

    Text Solution

    |

  11. Compute the following 3 × 4! + 7 × 4!

    Text Solution

    |

  12. Consider f, g and h be three real valued function defined on R. Let f(...

    Text Solution

    |

  13. Consider f, g and h be three real valued function defined on R. Let ...

    Text Solution

    |

  14. Compute (8!)/(4!) , Is (8!)/(4!) = 21?

    Text Solution

    |

  15. Consider f,g and h be three real valued functions defined on R. Let f(...

    Text Solution

    |

  16. Find the value of (20!)/(18! (20 - 18)!)

    Text Solution

    |

  17. Consider f,g and h be three real valued functions defined on R. Let f(...

    Text Solution

    |

  18. Consider f,g and h be three real valued differentiable functions defin...

    Text Solution

    |

  19. Find the intervals in which f(x)=(x-1)^2(x-2)^3 is increasing or decre...

    Text Solution

    |

  20. Consider f,g and h be three real valued differentiable functions defin...

    Text Solution

    |