Home
Class 12
MATHS
The value of a for which the function f(...

The value of `a` for which the function `f(x)=asinx+(1/3)sin3x` has an extremum at `x=pi/3` is 1 (b) `-1` (c) 0 (d) 2

A

1

B

-1

C

0

D

2

Text Solution

Verified by Experts

The correct Answer is:
5
If f(x) has an extremum at x=` pi//3` then f(X) =0 at q x=`pi//3`
Now f(X) = `a sinx +(1)/(3)` sin 3x
`therefore` f(x)=a cos x + cos 3x
`f'(pi//3)`=0`
or a=2
Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Multiple)|40 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise (Comprehension)|42 Videos

  • MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS

    CENGAGE|Exercise Exercise 6.7|5 Videos

  • METHODS OF DIFFERETIATION

    CENGAGE|Exercise Question Bank|29 Videos

  • MONOTONOCITY AND NAXINA-MINIMA OF FUNCTIONS

    CENGAGE|Exercise Comprehension Type|6 Videos

Similar Questions

Explore conceptually related problems

The value of a 'for which the function f(x)=a sin x+(1)/(3)sin3x has an extremum at x=(pi)/(4) is

The value of a for which the function f(x)=a sin x+((1)/(3))sin3x has an extremum at x=(pi)/(3) is 1(b)-1(c)0(d)2

What is the value of p for which the funtion f(X)=p sinx+(sin 3x)/(3) has an extremum at x=(pi)/(3) ?

The function f(x)=asinx+1/3 sin3x has maximum value at x=pi//3 . The value of a , is

The function f(x) = a sin x + 1/3 sin 3x has maximum value at x = pi/3 , the value of a is

CENGAGE-MONOTONICITY AND MAXIMA MINIMA OF FUNCTIONS-Exercise (Single)
  1. The global maximum value of f(x0=(log)(10)(4x^3-12 x^2+11 x-3),x in [2...

    Text Solution

    |

  2. f:R rarr R,f(x) is differentiable such that f(x)=k(x^(5)+x).(kne0) The...

    Text Solution

    |

  3. The value of a for which the function f(x)=asinx+(1/3)sin3x has an ext...

    Text Solution

    |

  4. If f(x)=alog|x|+b x^2+x has its extremum values at x=-1a n dx=2, then ...

    Text Solution

    |

  5. If a function f(x) has f^(prime)(a)=0a n df^(a)=0, then x=a is a maxim...

    Text Solution

    |

  6. The function f(x)=sin^4x +cos ^4 x increases if

    Text Solution

    |

  7. If f(x) =sin^(4)x+cos^(4)x increases, if

    Text Solution

    |

  8. If f(x)=x^5-5x^4+5x^3-10 has local maximum and minimum at x=pa n dx=q ...

    Text Solution

    |

  9. Let P(x)=a0+a1x^2+a2x^4++an x^(2n) be a polynomial in a real variable ...

    Text Solution

    |

  10. Let f(x) ={|x|for 0< |x| , 2 for x=0

    Text Solution

    |

  11. If f(x)=x^3+b x^2+c x+d and 0<b^2<c , then f(x) is a strictly increasi...

    Text Solution

    |

  12. If f(x)={(sin(x^(2)-3x),xle0 .^x+5x^(2),xgt0

    Text Solution

    |

  13. The greatest value of f(x)=cos(x e^([x])+7x^2-3x),x in [-1,oo], is (wh...

    Text Solution

    |

  14. The function f(x)=(4sin^2x-1)^n(x^2-x+1),n in N , has a local minimum...

    Text Solution

    |

  15. The true set of real values of x for which the function f(x)=xlnx-x+1 ...

    Text Solution

    |

  16. All possible value of f(x)=(x+1)^(1/3)-(x-1)^(1/3) on [0,1] is 1 (b) ...

    Text Solution

    |

  17. The function f(x)=(ln(pi+x))/(ln(e+x)) is increasing in (0,oo) decrea...

    Text Solution

    |

  18. If the function f(x)=2x^3-9a x^2+12 x^2x+1,w h e r ea >0, attains its ...

    Text Solution

    |

  19. Let f(x)={x+2,-1lelt0 1,x=0 (x)/(2),0ltxle1

    Text Solution

    |

  20. If f(x)={sin^(-1)(sinx),xgt0 (pi)/(2),x=0,then cos^(-1)(cosx),xlt0

    Text Solution

    |