Home
Class 12
MATHS
If x and y are strictly positive such th...

If x and y are strictly positive such that x+y =1, then the minimum value of x log x + y log y is

A

log 2

B

(-log 2)

C

2 log 2

D

0

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • MATRICES AND DETERMINANTS

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|367 Videos

  • MEASUREMENT OF ANGLES, TRIGONOMETRIC RATIOS AND RELATION BETWEEN SIDES AND ANGLES OF A TRIANGLE

    HIMALAYA PUBLICATION|Exercise QUESTION BANK|251 Videos

Similar Questions

Explore conceptually related problems

Find the general solution of y log y dx - x dy = 0

If x^(y) = log x , the value of dy/dx at x = e is

If log_(10)x + log_(10) y ge 2 , then the smallest value of x + y is :

Solve (y log x-1)y dx=xdy .

Draw graph of y=log(-x), when the graph of y=log(x) is given.

If x, y, z being positive |[1, log _x y,log _x z],[log _y x,1,log _y z],[log _z x,log _z y, 1]|=

Draw the graph of y=-log(x) when the graph of y=logx is known.

For all positive values of x and y, the value of ((1+x+x^(2))(1+y+y^(2)))/(xy)

HIMALAYA PUBLICATION-MAXIMA AND MINIMA-QUESTION BANK
  1. The maximum value of f(x) = 2x^(3) -21 x^(2) +36x +20 in 0 le x le 2

    Text Solution

    |

  2. The minium distance from the point (4,2) to the curve y^(2)=8x, is equ...

    Text Solution

    |

  3. If x and y are strictly positive such that x+y =1, then the minimum va...

    Text Solution

    |

  4. If x+y = 12, then the minimum value of x^(2) + y^(2) is

    Text Solution

    |

  5. If l^(2) + m^(2) =1, then the maximum value of l+m is

    Text Solution

    |

  6. The minimum value of x^(x) is

    Text Solution

    |

  7. The maximum value of xy subjects to x+y =7 is

    Text Solution

    |

  8. The minimum value of (x- alpha)(x-beta) is

    Text Solution

    |

  9. Show that y = log(1 +x) - (2x)/(2 + 2x) , x gt -1, is an increasing fu...

    Text Solution

    |

  10. The function f(x) = xe^(-x) (x in R) attains a maximum value at x =

    Text Solution

    |

  11. Observe the following statements: A : f(x) = 2x^(3)-9x^(2)+12x-3 is in...

    Text Solution

    |

  12. If x is real then the minimum value of (x^(2)-x+1)/(x^(2)+x+1) is

    Text Solution

    |

  13. The perimeter of a sector is a constant . If its area is to be maximum...

    Text Solution

    |

  14. In the interval (-3,3) the function f(x) = x/3 + 3/x, x ne 0 is

    Text Solution

    |

  15. The function f(x) = 1-x^(3)-x^(5) is decreasing for

    Text Solution

    |

  16. If PQ and PR are the two sides of a triangle, then the angle between t...

    Text Solution

    |

  17. The function y = a(1-cosx) is maximum when x is equal to

    Text Solution

    |

  18. Twenty metres are available to fence a flower bed in the form of a cir...

    Text Solution

    |

  19. The function f(x) = tan^(-1) (sin x + cos x), x gt 0 is always an incr...

    Text Solution

    |

  20. The maximum value of xy, when x+2y = 8 is

    Text Solution

    |