Home
Class 12
MATHS
If a x+b/xgeqc for all positive x where ...

If `a x+b/xgeqc` for all positive `x` where `a ,\ b ,\ >0` , then `a b<(c^2)/4` (b) `geq(c^2)/4` (c) `a bgeqc/4` (d) none of these

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • LINEAR PROGRAMMING

    RD SHARMA ENGLISH|Exercise All Questions|144 Videos

  • MEAN AND VARIANCE OF A RANDOM VARIABLE

    RD SHARMA ENGLISH|Exercise All Questions|125 Videos

Similar Questions

Explore conceptually related problems

If ax+b/x >= c for all positive x, where a, b, c > 0, then-

If ax+b/x >= c for all positive x, where a, b, c > 0, then-

If a x^2+b/xgeqc for all positive x where a >0 and b >0, show that 27 a b^2geq4c^3dot

If a x^2+b/xgeqc for all positive x where a >0 and b >0, show that 27 a b^2geq4c^3dot

If x^a=y^b=c^c , where a,b,c are unequal positive numbers and x,y,z are in GP, then a^3+c^3 is :

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(1/(a b))\ ((x^b)/(x^c))^(1/(b c))\ \ ((x^c)/(x^a))^(1/(a c))=1

Assuming that x is a positive real number and a ,\ b ,\ c are rational numbers, show that: ((x^a)/(x^b))^(a+b)\ ((x^b)/(x^c))^(b+c)((x^c)/(x^a))^(c+a)=1

If a , b , c are positive numbers such that a gt b gt c and the equation (a+b-2c)x^(2)+(b+c-2a)x+(c+a-2b)=0 has a root in the interval (-1,0) , then

If f(a-x)=f(a+x) " and " f(b-x)=f(b+x) for all real x, where a, b (a gt b gt 0) are constants, then prove that f(x) is a periodic function.

If f(a-x)=f(a+x) " and " f(b-x)=f(b+x) for all real x, where a, b (a gt b gt 0) are constants, then prove that f(x) is a periodic function.

RD SHARMA ENGLISH-MAXIMA AND MINIMA-All Questions
  1. Write the maximum value of f(x)=(logx)/x , if it exists.

    Text Solution

    |

  2. The maximum value of x^(1/x),x &gt;0 is (a)e^(1/e) (b) (1/e)^e (c)...

    Text Solution

    |

  3. If a x+b/xgeqc for all positive x where a ,\ b ,\ >0 , then a b<(c^2)/...

    Text Solution

    |

  4. The minimum value of x/((log)e x) is e (b) 1//e (c) 1 (d) none of thes...

    Text Solution

    |

  5. For the function f(x)=x+1/x x=1 is a point of maximum (b) x=-1 is a p...

    Text Solution

    |

  6. Let f(x)=x^3+3x^2-9x+2 . Then, f(x) has a maximum at x=1 (b) a minimum...

    Text Solution

    |

  7. The minimum value of f(x)=x^4-x^2-2x+6 is (a) 6 (b) 4 (c) 8 (d) none o...

    Text Solution

    |

  8. The number which exceeds its square by the greatest possible quanti...

    Text Solution

    |

  9. Let f(x)=(x-a)^2+(x-b)^2+(x-c)^2 . Then, f(x) has a minimum at x= (a+...

    Text Solution

    |

  10. The sum of two non-zero numbers is 8, the minimum value of the sum ...

    Text Solution

    |

  11. The function f(x)=sum(r=1)^5(x-r)^2 assuming minimum value at x= ...

    Text Solution

    |

  12. At x=(5pi)/6,\ \ f(x)=2sin3x+3cos3x is (a) 0 (b) maximum (c) minimum (...

    Text Solution

    |

  13. If x lies in the interval [0,\ 1] , then the least value of x^2+x+1...

    Text Solution

    |

  14. The least value of the function f(x)=x^3-18 x^2+96 x in the interval [...

    Text Solution

    |

  15. The maximum value of f(x)=x/(4+x+x^2) on [-1,1] is (a)1/4 (b) -1/3 (c)...

    Text Solution

    |

  16. Find the point on the curve y^2=4x which is nearest to the point (2, 1...

    Text Solution

    |

  17. If x+y=8 , then the maximum value of x y is (a) 8 (b) 16 (c) 20 (d)...

    Text Solution

    |

  18. The least and greatest values of f(x)=x^3-6x^2+9x in [0,\ 6] , are ...

    Text Solution

    |

  19. f(x)=sin+sqrt(3)cosx is maximum when x= pi/3 (b) pi/4 (c) pi/6 (d) 0

    Text Solution

    |

  20. If a cone of maximum volume is inscribed in a given sphere, then th...

    Text Solution

    |