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)`

Text Solution

Verified by Experts

Answer is C)
We have
` f(x)=x^{x}={Let}(y)`
Taking log on both sides
` log (y)=x log x`
` frac{1}{y} times frac{d y}{d x}=1+log x`
` frac{d y}{d x}=x^{x}(1+log x)`
Function is decreasing,
` ...
Promotional Banner

Topper's Solved these Questions

  • HIGHER ORDER DERIVATIVES

    RD SHARMA|Exercise Solved Examples And Exercises|176 Videos

  • INDEFINITE INTEGRALS

    RD SHARMA|Exercise Solved Examples And Exercises|1401 Videos

Similar Questions

Explore conceptually related problems

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

Let f:[(1)/(2),1]rarr R (the set of all real numbers) be a positive,non-constant,and differentiable function such that f'(x)<2f(x) and f((1)/(2))=1. Then the value of int_((1)/(2))^(1)f(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))

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

If the function f(x)={(cosx)^(1/x),x!=0k ,x=0 is continuous at x=0 , then the value of k is 0 (b) 1 (c) -1 (d) e

Let f(x)=int_(0)^(x)e^(t)(t-1)(t-2)dt. Then, f decreases in the interval

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

The function f(x)={{:(,(e^(1/x)-1)/(e^(1/x)+1),x ne 0),(,0,x=0):}

Let f,\ g\ a n d\ h be real-valued functions defined on the interval [0,\ 1] by f(x)=e^x^2+e^-x^2,\ g(x)=x e^x^2+e^-x^2\ a n d\ h(x)=x^2e^x^2+e^-x^2 . If a , b ,\ a n d\ c denote respectively, the absolute maximum of f,\ g\ a n d\ h on [0,\ 1], then a=b\ a n d\ c!=b (b) a=c\ a n d\ a!=b a!=b\ a n d\ c!=b (d) a=b=c

A Function f(x) satisfies the relation f(x)=e^(x)+int_(0)^(1)e^(x)f(t)dt* Then (a)f(0) 0

RD SHARMA-INCREASING AND DECREASING FUNCTION -Solved Examples And Exercises
  1. The interval of increase of the function f(x)=x-e^x+tan(2pi//7) is (a)...

    Text Solution

    |

  2. The function f(x)=cot^(-1)x+x increases in the interval (a) (1,\ oo) ...

    Text Solution

    |

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

    Text Solution

    |

  4. The function f(x)=2log(x-2)-x^2+4x+1 increases on the interval (a) (1,...

    Text Solution

    |

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

    Text Solution

    |

  6. IF f(x)=x^3+a x^2+b x+5sin^2x\ is a strictly increasing functio...

    Text Solution

    |

  7. The function f(x)=(log)e(x^3+sqrt(x^6+1)) is of the following types: (...

    Text Solution

    |

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

    Text Solution

    |

  9. Let f(x)=tan^(-1)(g(x)) , where g(x) is monotonically increasing for 0...

    Text Solution

    |

  10. Let f(x)=x^3-6x^2+15 x+3 . Then, (a) f(x)>0 for all x in R (b) f(x)>...

    Text Solution

    |

  11. The function f(x)=x^2\ e^(-x) is monotonic increasing when (a) x in R...

    Text Solution

    |

  12. Function f(x)=cosx-2\ lambda\ x is monotonic decreasing when (a) lambd...

    Text Solution

    |

  13. In the interval (1,\ 2) , function f(x)=2|x-1|+3|x-2| is (a) monotonic...

    Text Solution

    |

  14. Function f(x)=x^3-27 x+5 is monotonically increasing when (a) x<-3 (b...

    Text Solution

    |

  15. Function f(x)=2x^3-9x^2+12 x+29 is monotonically decreasing when (a) x...

    Text Solution

    |

  16. If f(x)=k x^3-9x^2+9x+3 monotonically increasing in R , then k<3 (b) ...

    Text Solution

    |

  17. f(x)=2x-tan^(-1)x-log{x+sqrt(x^2+1)} is monotonically increasing when ...

    Text Solution

    |

  18. Function f(x)=|x|-|x-1| is monotonically increasing when (a) x<0 (b) ...

    Text Solution

    |

  19. Every invertible function is (a) monotonic function          (b) co...

    Text Solution

    |

  20. In the interval (1,\ 2) , function f(x)=2|x-1|+3|x-2| is (a) increasin...

    Text Solution

    |