Home
Class 12
MATHS
Show that the maximum value of (1/x)^...

Show that the maximum value of `(1/x)^x` is `e^(1//e)` .

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

Show that (logx)/x has a maximum value at x=e .

The maximum value of x^(1/x),x >0 is (a) e^(1/e) (b) (1/e)^e (c) 1 (d) none of these

The maximum value of x^(1/x),x >0 is (a) e^(1/e) (b) (1/e)^e (c) 1 (d) none of these

Find the maximum value of the function x * e^(-x) .

The maximum value of (logx)/x is (a) 1 (b) 2/e (c) e (d) 1/e

Given the function f(x)=x^2e^-(2x) ,x>0. Then f(x) has the maximum value equal to a) e^-1 b) (2e)^-1 . c) e^-2 d) none of these

The minimum value of x\ (log)_e x is equal to e (b) 1//e (c) -1//e (d) 2e (e) e

The minimum value of x/((log)_e x) is e (b) 1//e (c) 1 (d) none of these

The minimum value of e^((2x^2-2x+1)sin^(2)x) is a. e (b) 1/e (c) 1 (d) 0

The maximum value of x^4e^ (-x^2) is (A) e^2 (B) e^(-2) (C) 12 e^(-2) (D) 4e^(-2)

RD SHARMA ENGLISH-MAXIMA AND MINIMA-All Questions
  1. It is given that at x=1 , the function x^4-62 x^2+a x+9 attains its ma...

    Text Solution

    |

  2. If y=(a x-b)/((x-1)(x-4)) has a turning point P(2,\ -1) , find the val...

    Text Solution

    |

  3. Show that the maximum value of (1/x)^x is e^(1//e) .

    Text Solution

    |

  4. Show that sin^p\ theta\ cos^q\ theta attains a maximum, when theta...

    Text Solution

    |

  5. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  6. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  7. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  8. Find the points of local maxima or minima and corresponding local ma...

    Text Solution

    |

  9. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  10. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  11. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  12. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  13. Find the points of local maxima or minima and corresponding local ma...

    Text Solution

    |

  14. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  15. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  16. Find the points of local maxima or minima and corresponding local m...

    Text Solution

    |

  17. Find the local extremum values of the following functions: f(x)=(x-1...

    Text Solution

    |

  18. The function y=alogx+b x^2+x has extreme values at x=1 and x=2 . Find ...

    Text Solution

    |

  19. Show that (logx)/x has a maximum value at x=e .

    Text Solution

    |

  20. Find the maximum and minimum values of the function f(x)=4/(x+2)+x ...

    Text Solution

    |