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

Find two positive numbers x and y, such that `x+y=64` and `x^(3)+y^(3)` is minimum.

Text Solution

Verified by Experts

The correct Answer is:
32, 32
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK BASED MCQS|83 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise TEXTBOOK ILLUSTRATIONS FOR PRACTICE WORK|51 Videos

  • APPLICATION OF DERIVATIVES

    KUMAR PRAKASHAN|Exercise MISCELANEOUS EXERCISE - 6|27 Videos

  • ANNUAL EXAMINATION :SAMPLE PAPER

    KUMAR PRAKASHAN|Exercise PART-B ( SECTION-C)|10 Videos

  • APPLICATION OF INTEGRALS

    KUMAR PRAKASHAN|Exercise PRACTICE PAPER ( SECTION -D)|2 Videos

Similar Questions

Explore conceptually related problems

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

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

If two positive integers a and b are expressible as a = x^(3) y and b = x^(2) y^(3) x and y being prime numbers, then HCF (a, b) is ..........

The A.M of two positive number is x and two G.M.'s between them are y and z. Then (y^(3) + z^(3))/(xyz) = …….

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 a relation between x and y such that the point (x,y) is equidistant from the point (3,6) and (-3, 4).

Let [a] denotes the larger integer not exceeding the real number a if x and y satisfy the equations y=2[x]+3 and y=3[x-2[ simultaneously determine [x+y]

Factorise : 125x^(3) - 64y^(3)

Factorise : 64x^(3) + 125y^(3)

If x= 5 and y=2 find the values of : (x^(y)+ y^(x) )

KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -PRACTICE WORK
  1. At what points, f(x)=1+2 sin x + 3 cos^(2)x, 0 lt x lt (2pi)/(3) has m...

    Text Solution

    |

  2. Divide 20 into two parts such that the product of one part and the cub...

    Text Solution

    |

  3. Find two positive numbers x and y, such that x+y=64 and x^(3)+y^(3) is...

    Text Solution

    |

  4. What is the maximum slope of the curve y=-x^(3)+3x^(2)+2x-27 ? Also fi...

    Text Solution

    |

  5. Find the co-ordinates of a point on the parabola y=x^(2)+7x+2 which is...

    Text Solution

    |

  6. The total area of a page is 150 square inchese. The combined width of ...

    Text Solution

    |

  7. The three sides of a trapezium are equal, each being 6 cm long. Find t...

    Text Solution

    |

  8. In a right angle triangle, the sum of hypotenuous and one side is give...

    Text Solution

    |

  9. Show that a triangle of maximum area that can be inscribed in a circle...

    Text Solution

    |

  10. The circle x^(2)+y^(2)=1 cats the X - axis at P and Q. Another circle ...

    Text Solution

    |

  11. Two roads OA and OB intersect at an angle 60^(@). A car driver approac...

    Text Solution

    |

  12. Find the interval in which the function f(x)=x^(4)+32x is increasing o...

    Text Solution

    |

  13. Show that the curves xy=a^(2) and x^(2)+y^(2)=2a^(2) touch each other.

    Text Solution

    |

  14. Prove that the slope of tangent at any point of the curve y=6x?^(3)+15...

    Text Solution

    |

  15. Prove that f(x)=((1)/(x))^(x) has local maximum at x=(1)/(e ).x in R^(...

    Text Solution

    |

  16. For simple pendulum, T = 2pi sqrt((l)/(g)) where T is the periodic tim...

    Text Solution

    |

  17. Find the equation of normal to the curve x^((2)/(3))+y^((2)/(3))=a^((2...

    Text Solution

    |

  18. Prove that the function f(x)=2|x-1|+3|x-4| is decreasing in the intrer...

    Text Solution

    |

  19. The radius of the cone is increasing at the rate of 4 cm/se. Its heigh...

    Text Solution

    |

  20. Prove that in all rectangles with given area, the perimeter of square ...

    Text Solution

    |