Home
Class 12
MATHS
Find two positive numbers x and y such t...

Find two positive numbers x and y such that x + y = 60 and `xy^(3)` is maximum.

Text Solution

Verified by Experts

The correct Answer is:
45,45
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    NCERT TAMIL|Exercise EXERCISE 6.6|24 Videos

  • APPLICATION OF DERIVATIVES

    NCERT TAMIL|Exercise EXERCISE 6.4|23 Videos

  • APPLICATION OF INTEGRALS

    NCERT TAMIL|Exercise Miscellaneous Exercise|19 Videos

Similar Questions

Explore conceptually related problems

Find two positive numbers x and y such that their sum is 35 and the product x^(2) y^(5 ) is a maximum.

If x,y,z are positive numbers in A.P., then

If x,y,z are positive real numbers such that x^(2)+y^(2)+Z^(2)=7 and xy+yz+xz=4 then the minimum value of xy is

Find the number of positive integral solutions of x y z=21600.

If x and y are positive real numbers such that 2log(2y - 3x) = log x + log y," then find the value of " x/y .

Find the total number of positive integral solutions for (x ,y ,z) such that x y z=24. Also find out the total number of integral solutions.

Find x^(3) - y^(3) , find x - y =5 and xy = 14

Let f be a function defined from F^(+)rarrR^(+). If (f(xy))^(2)=x(f(y))^(2) for all positive numbers x and y, If f(2)=6, find f(50) =?

If x ,y ,a n dz are positive real umbers and x=(12-y z)/(y+z) . The maximum value of x y z equals.

Let x, y be positive real numbers and m, n be positive integers, The maximum value of the expression (x^(m)y^(n))/((1+x^(2m))(1+y^(2n))) is

NCERT TAMIL-APPLICATION OF DERIVATIVES-EXERCISE 6.5
  1. Find the maximum value of 2x^(3) – 24x + 107 in the interval [1, 3]. F...

    Text Solution

    |

  2. It is given that at x = 1, the function x^(4) – 62x^(2) + ax + 9 attai...

    Text Solution

    |

  3. Find the maximum and minimum values of x + sin 2x on [0, 2pi].

    Text Solution

    |

  4. Find two numbers whose sum is 24 and whose product is as large as poss...

    Text Solution

    |

  5. Find two positive numbers x and y such that x + y = 60 and xy^(3) is m...

    Text Solution

    |

  6. Find two positive numbers x and y such that their sum is 35 and the pr...

    Text Solution

    |

  7. Find two positive numbers whose sum is 16 and the sum of whose cubes i...

    Text Solution

    |

  8. A square piece of tin of side 18 cm is to be made into a box without t...

    Text Solution

    |

  9. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box wit...

    Text Solution

    |

  10. Show that of all the rectangles inscribed in a given fixed circle, the...

    Text Solution

    |

  11. Show that the right circular cylinder of given surface and maximum vol...

    Text Solution

    |

  12. Of all the closed cylindrical cans (right circular), of a given volume...

    Text Solution

    |

  13. A wire of length 28 m is to be cut into two pieces. One of the pieces ...

    Text Solution

    |

  14. Prove that the volume of the largest cone that can be inscribed in a s...

    Text Solution

    |

  15. Show that the right circular cone of least curved surface and given vo...

    Text Solution

    |

  16. Show that the semi-vertical angle of the cone of the maximum volume an...

    Text Solution

    |

  17. Show that semi-vertical angle of right circular cone of given surface ...

    Text Solution

    |

  18. The point on the curve x^(2) = 2y which is nearest to the point (0, 5)...

    Text Solution

    |

  19. For all real values of x, the minimum value of (1-x+x^(2))/(1+x+x^(2))...

    Text Solution

    |

  20. The maximum value of [ x(x-1)+1]^((1)/(3)) , 0 lt= x lt= 1 is

    Text Solution

    |