Home
Class 12
MATHS
Let f(x) = cos 2pix + x -[x]([*] denotes...

Let `f(x) = cos 2pix + x -[x]([*]` denotes the greatest integer function). Then number of points in `[0,10]` at which f(x) assumes its local maximum value, is

A

0

B

10

C

9

D

Infinite

Text Solution

Verified by Experts

The correct Answer is:
B
we have
`f(x)=cos 2 pi x + x -[x] " for all " x in [0,10]`
`rArr f'(x) =0 rArr sin 2 pi x +1 " for all " x in underset(k=0)overset(9)cup (k,k+1)`
`f'(x) =0 rArr sin 2 pi x = 1/(2pi)`
Clearly this equation has two solutions in each of the sub-intervals (k,k+1) where k= 0,1,2,......9
Since points of maxima and minima occur alternately.
Therefore ,out of 20 points , there are 10 points of local maxima and 10 points of local minima.
Promotional Banner

Topper's Solved these Questions

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Section II - Assertion Reason Type|7 Videos

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Exercise|50 Videos

  • MAXIMA AND MINIMA

    OBJECTIVE RD SHARMA|Exercise Chapter Test|30 Videos

  • MATHEMATICAL REASONING

    OBJECTIVE RD SHARMA|Exercise Chapter Test|20 Videos

  • MEASURES OF CENTRAL TENDENCY

    OBJECTIVE RD SHARMA|Exercise Chapter Test|21 Videos

Similar Questions

Explore conceptually related problems

Let f(x)=cos2 pi x+x-[x](*] denotes the greatest integer function).Then number of points in [0,10] at which f(x) assumes its local maximum value,is

Let f(x)=[x]+sqrt(x-[x]), where [.] denotes the greatest integer function.Then

f(x)=log(x-[x]), which [,] denotes the greatest integer function.

If f(x)=[sin^(2) x] ([.] denotes the greatest integer function), then

Let f(x)=(-1)^([x]) where [.] denotes the greatest integer function),then

Let f(x)=sec^(-1)[1+cos^(2)x], where [.] denotes the greatest integer function. Then the

Let f(x) = [x]^(2) + [x+1] - 3 , where [.] denotes the greatest integer function. Then

Let f(x)=cos x and g(x)=[x+1],"where [.] denotes the greatest integer function, Then (gof)' (pi//2) is

If f(x)=[2x], where [.] denotes the greatest integer function,then

Let f(x)=[|x|] where [.] denotes the greatest integer function, then f'(-1) is

OBJECTIVE RD SHARMA-MAXIMA AND MINIMA -Section I - Solved Mcqs
  1. Let f(x)=a x^3+b x^2+c x+1 has exterma at x=alpha,beta such that alpha...

    Text Solution

    |

  2. P=x^3-1/x^3, Q=x-1/x x in (1,oo) then minimum value of P/(sqrt(3)Q^2...

    Text Solution

    |

  3. Let f(x) = cos 2pix + x -[x]([*] denotes the greatest integer function...

    Text Solution

    |

  4. Let f(x)=a-(x-3)^(8//9) then greatest value of f(x) is

    Text Solution

    |

  5. A function f such that f'(a)=f''(a)=….=f^(2n)(a)=0 , and f has a l...

    Text Solution

    |

  6. Let f(x)={{:(3x^2-2x+10, x lt 1),(-2,x gt 1):} The set of values of ...

    Text Solution

    |

  7. The maximum value of cos (int(2x)^(x^(2)) e^t sin^2 " t dt ")

    Text Solution

    |

  8. Let f(x)= {{:(1+ sin x, x lt 0 ),(x^2-x+1, x ge 0 ):}

    Text Solution

    |

  9. Let f(x)=x^(n+1)+ax^n, "where " a gt 0. Then, x=0 is point of

    Text Solution

    |

  10. The greph of y=x^3+ax^2+bx+c has no extemun if and only if

    Text Solution

    |

  11. If f(x) =int(x)^(x^2) (t-1)dt, 1 le x le 2 then the greatest value of ...

    Text Solution

    |

  12. If the parabola y=ax^2+bx+c has vertex at(4,2)and a in [1,3] then the...

    Text Solution

    |

  13. Let f(X)=In (2x -x^2)+ sin (pix)/(2). Then which one of the following ...

    Text Solution

    |

  14. If alpha and beta respectively the minmum and minimum values of the fu...

    Text Solution

    |

  15. Let f(x)={{:(x^2+4x "," -3 le x le 0),(-sin x ","0 lt x le pi//2 ),(...

    Text Solution

    |

  16. If alpha be the number of solutions of the equation [sin x] =|x| ) and...

    Text Solution

    |

  17. Let f(x1,x2,x3,x4)=x1^2+x2^2+x3^2+x4^2-2(x1+x2+x3+x4)+10 and x1,x3 i...

    Text Solution

    |

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

    Text Solution

    |

  19. Let f be a function defined on R (the set of all real numbers) such th...

    Text Solution

    |

  20. Let f:R to R be defined by f(x)={{:(2k-2x",",ifxle-1),(2x+3",",iffxg...

    Text Solution

    |