Home
Class 12
MATHS
The function f(x)=x^x decreases on the i...

The function `f(x)=x^x` decreases on the interval (a) `(0,\ e)` (b) `(0,\ 1)` (c) `(0,\ 1//e)` (d) `(1//e ,\ e)`

A

(0,e)

B

(0,1)

C

`90,1//e)

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
C
Clearly , f(x) is defined for all xgt0 Now
`f(x) =x^x rArr f'(x) = x^x(1+logx)`
For f(x) to be decresing , we must have ,
f'(x) lt 0
`rArr x^x(1+logx)lt 0`
`rArr 1+logxlt 0`
`rArr logx lt-1 rArr xlte^(-1)`
So f(x) is decreasing on `(0,1//e)`
Promotional Banner

Topper's Solved these Questions

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Section II - Assertion Reason Type|8 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|36 Videos

  • INCREASING AND DECREASING FUNCTIONS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|18 Videos

  • HEIGHTS AND DISTANCES

    OBJECTIVE RD SHARMA ENGLISH|Exercise Exercise|45 Videos

  • INDEFINITE INTEGRALS

    OBJECTIVE RD SHARMA ENGLISH|Exercise Chapter Test|30 Videos

Similar Questions

Explore conceptually related problems

The function x^x decreases in the interval (a) (0,e) (b) (0,1) (c) (0,1/e) (d) none of these

The interval of increase of the function f(x)=x-e^x+tan(2pi//7) is (a) (0,\ oo) (b) (-oo,\ 0) (c) (1,\ oo) (d) (-oo,\ 1)

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x)a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) (c) ((e-1)/2,e-1) (d) (0,(e-1)/2)

The value of the integral int_0^1e^x^2_dx lies in the interval (a) (0,1) (b) (-1,0) (c) (1, e) (d) none of these

The mean value of the function f(x)= 2/(e^x+1) in the interval [0,2] is

Let f:[1/2,1]->R (the set of all real numbers) be a positive, non-constant, and differentiable function such that f^(prime)(x)<2f(x))a n df(1/2)=1 . Then the value of int_(1/2)^1f(x)dx lies in the interval (a) (2e-1,2e) (b) (3-1,2e-1) ((e-1)/2,e-1) (d) (0,(e-1)/2)

The domain of f(x) is (0,1) Then the domain of (f(e^x)+f(1n|x|) is (a) (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

f(x)=|x log_e x| monotonically decreases in (0,1/e) (b) (1/e ,1) (1,oo) (d) (1/e ,oo)

The domain of f(x) is (0,1) .Then the domain of (f(e^x)+f(1n|x|) is (a) (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

The domain of f(x) is (0,1)dot Then the domain of (f(e^x)+f(1n|x|) is a. (-1, e) (b) (1, e) (c) (-e ,-1) (d) (-e ,1)

OBJECTIVE RD SHARMA ENGLISH-INCREASING AND DECREASING FUNCTIONS-Section I - Solved Mcqs
  1. Find the interval to which b may belong so that the function f(x)=...

    Text Solution

    |

  2. The interval of increase of the function f(x)=x-e^x+tan(2pi//7) is (a)...

    Text Solution

    |

  3. The function f(x)=x^x decreases on the interval (a) (0,\ e) (b) (0,\ ...

    Text Solution

    |

  4. The set of all x for which log(1+ x) le x is equal to …… .

    Text Solution

    |

  5. The function f(x)=x/(xlogx) increase on the interval

    Text Solution

    |

  6. The function f(x)=tan^(-1)(sinx+cosx) is an increasing function in (-p...

    Text Solution

    |

  7. The set of all x for which 1+logx lt x, is

    Text Solution

    |

  8. For x gt 1 and y = lod x which one of the following is not true ?

    Text Solution

    |

  9. If the function f(x)=2x^2-k x+5 is increasing on [1,\ 2] , then k lies...

    Text Solution

    |

  10. Let f(x)=x^3+a x^2+b x+5sin^2x be an increasing function on the set Rd...

    Text Solution

    |

  11. If a ,\ b ,\ c are real numbers, then find the intervals in which f(...

    Text Solution

    |

  12. Let f(x) be the function given by f(x) = 3x^5-5x^3+21x+3sinx+cosx+5....

    Text Solution

    |

  13. If the function f(x)=2tanx+(2a+1)(log)e|secx|+(a-2)x is increasing on ...

    Text Solution

    |

  14. If f'(x^2-4x+3)gt0 " for all " x in (2,3) then f(sinx) is increasing ...

    Text Solution

    |

  15. Let f(x) = tan^-1 (g(x)), where g (x) is monotonically increasing for...

    Text Solution

    |

  16. Let f(x) =inte^x(x-1)(x-2)dx, then f(x) decrease in the interval

    Text Solution

    |

  17. Assertion Consider the following statements in S and R S: Both sinx a...

    Text Solution

    |

  18. The length of the longest interval, in which the function 3sin x-4 sin...

    Text Solution

    |

  19. If f(x)=x^3+4x^2+ax+5 is a monotonically decreasing function of x in t...

    Text Solution

    |

  20. Let f(x) = 2sin^3x-3sin^2+12sinx+5, 0lexlepi/2 Then f(x)is

    Text Solution

    |