Home
Class 12
MATHS
The greatest value of the fucntion f(x)=...

The greatest value of the fucntion `f(x)=sin^(-1)x^2` in interval `[-1//sqrt(2),1//sqrt(2)]` is

A

`pi/3`

B

`pi/2`

C

`-pi/2`

D

`-pi/3`

Text Solution

Verified by Experts

The correct Answer is:
D
We have
`f(x)=sin^(-1)""x^2 rArr f'(x) = (2x)/(sqrt(1-x^4))`
`therefore f(x) =0 rArr x=0`
Now
`f(-1/sqrt(2))=sin^(-1)""1/2=pi/6,f(1/sqrt(2))=sin ^(-1)1/2=pi/6,`
and `f(0)= sin^(-1)(0)=0`
Hence , the greatest value is `pi/6`
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

The greatest value of the function f(x)=tan^(-1)x-(1)/(2)log x in [(1)/(sqrt(3)),sqrt(3)] is

The least value of the f(x) given by f(x)=tan^(-1)x-1/2 log_ex " in the interval "[1//sqrt3,sqrt3] , is

The greatest value of the function f(x)=(sin2x)/(sin(x+(pi)/(4))) on the interval (0,(pi)/(2)) is (1)/(sqrt(2))(b)sqrt(2)(c)1(d)-sqrt(2)

The greatest value of f(x)=int_(1)^(x)|t||dt on the interval [-(1)/(2),(1)/(2)]:

Find the greatest & least value of f(x)=sin^(-1).(x)/(sqrt(x^(2)+1))-ln x in [(1)/(sqrt(3)), sqrt(3)] .

The greatest, the least values of the function , f(x) =2-sqrt(1+2x+x^(2)), x in [-2,1] are respectively

If x in[-1,(-1)/(sqrt(2))] , then the inverse of the function f(x)=sin^(-1)(2x sqrt(1-x^(2))) is given by

The greatest and the least value of the function, f(x)=sqrt(1-2x+x^(2))-sqrt(1+2x+x^(2)),x in(-oo,oo) are

Find the greatest and the least values of the following functions on the indicated intervals : f(x) = sqrt(4-x^(2)) " on " [-2,2]

STATEMENT-1: The values of f(x)=3sin(sqrt((pi^(2))/(16)-x^(2)) lie in the interval [0,(3)/(sqrt(3))]. and STATEMENT-2The domain of definition of the function f(x)=3sin(sqrt((pi^(2))/(16)-x^(2)) is [-(pi)/(4),(pi)/(4)]

OBJECTIVE RD SHARMA-MAXIMA AND MINIMA -Section I - Solved Mcqs
  1. In the interval (0,pi//2) the fucntion f(x)= tan^nx+cot^nx attains

    Text Solution

    |

  2. The fraction exceeds its p^(th) power by the greatest number possible...

    Text Solution

    |

  3. The greatest value of the fucntion f(x)=sin^(-1)x^2 in interval [-1//...

    Text Solution

    |

  4. The minimum value of the fuction f(x)=2|x-2|+5|x-3| for all x in R ,...

    Text Solution

    |

  5. The minimum value of the fuction f(x) given by f(x)=(x^m)/(m)+(x^(-...

    Text Solution

    |

  6. The largest term of the sequence lt an gt given by an=(n^2)/(n^3 +...

    Text Solution

    |

  7. Let f(x)=a x^3+b x^2+c x+1 has exterma at x=alpha,beta such that alpha...

    Text Solution

    |

  8. 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

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |