Home
Class 12
MATHS
If x^(2)+y^(2)+z^(2)=1"for " x,y,z inR, ...

If `x^(2)+y^(2)+z^(2)=1"for " x,y,z inR,` then the maximum value of `x^(3)+y^(3)+z^(3)-3xyz` is

A

`(1)/(2)`

B

1

C

2

D

3

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|7 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 2|4 Videos

  • MONOTONICITY MAXIMA AND MINIMA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|29 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

Divide 30x^(2)y^(3)z by -3xyz

If x=1, y=2 and z=3 , find the value of: x^3-z^3+y^3

If x, y, z in R are such that they satisfy x + y + z = 1 and tan^(-1)x+tan^(-1)y+tan^(-1)z=(pi)/(4) , then the value of |x^(3)+y^(3)+z^(3)-3| is

If xyz = 1 and x, y, z gt 0 then the minimum value of the expression (x+2y)(y+2z)(z+2x) is

If x+y+z=1 , then the minimum value of xy(x+y)^(2)+yz(y+z)^(2)+zx(z+x)^(2) is , where x,y,z inR^(+)

If x^(3)+y^(3)+z^(3)=3xyz and x+y+z=0, find the value of ((x+y)^(2))/(xy)=((y+z)^(2))/(yz) +((z+x)^(2))/(zx)

If x^(3) + y^(3) + z^(3) = 3xyz and x + y + z = 0 , find the value of : ((x+y)^(2))/(xy) + ((y+z)^(2))/(yz) + ((z+x)^(2))/(zx)

If x + y + z = 12, x^(2) + Y^(2) + z^(2) = 96 and (1)/(x)+(1)/(y)+(1)/(z)= 36 . Then find the value x^(3) + y^(3)+z^(3).

If x+y+z=8\ \ a n d\ \ \ x y+y z+z x=20 , find the value of x^3+y^3+z^3-3x y z

If x+y+z=1,x y+y z+z x=-1 and x y z=-1, find the value of x^3+y^3+z^3dot

ARIHANT MATHS ENGLISH-MONOTONICITY MAXIMA AND MINIMA-EXAMPLE
  1. Discuss the nature of following functions, graphically.

    Text Solution

    |

  2. Let f(x)=x^(3) find the point at which f(x) assumes local maximum and ...

    Text Solution

    |

  3. If x^(2)+y^(2)+z^(2)=1"for " x,y,z inR, then the maximum value of x^(3...

    Text Solution

    |

  4. A solid cylinder of height H has a conical portion of same height and ...

    Text Solution

    |

  5. Statement 1: f(x)=x+cosx is increasing AAx in Rdot Statement 2: If f...

    Text Solution

    |

  6. Consider a DeltaOAB formed by the point O(0,0),A(2,0),B(1,sqrt(3)).P(x...

    Text Solution

    |

  7. Let f(x)=ax^(2)+bx+c,ab,c in R. It is given |f(x)|le1,|x|le1 The po...

    Text Solution

    |

  8. Let f(x)=ax^(2)+bx+c,ab,c in R. It is given |f(x)|le1,|x|le1 The po...

    Text Solution

    |

  9. The absolute maximum and minimum values of functions can be found by t...

    Text Solution

    |

  10. The absolute maximum and minimum values of functions can be found by t...

    Text Solution

    |

  11. Let f(x)={:{(max{t^(3)-t^(2)+t+1,0letlex}",",0lexle1),(min{3-t,1lttlex...

    Text Solution

    |

  12. The graph of derivative of a function f(x) is given (i.e. y=f'(x)). An...

    Text Solution

    |

  13. If a function (continuos and twice differentiable) is always concave u...

    Text Solution

    |

  14. If f(x)={(1)/(x)}andg(x)={x^(2)}, then the number of positive roots sa...

    Text Solution

    |

  15. Match the Statements of Column I with values of Column II.

    Text Solution

    |

  16. Match the Statements of Column I with values of Column II.

    Text Solution

    |

  17. The set of all points where f(x) is increasing is (a,b)cup(c,oo). Find...

    Text Solution

    |

  18. Let f(x) be a cubic polynomial defined by f(x)=x^(3)/(3)+(a-3)x^(2)+...

    Text Solution

    |

  19. If f(x)=max| 2 siny-x|, (where y in R), then find the minimum value o...

    Text Solution

    |

  20. Let f(x)=sin^(-1)((2phi(x))/(1+phi^(2)(x))). Find the interval in whic...

    Text Solution

    |