Home
Class 12
MATHS
The function f(x) = x^x is minimum at x=...

The function `f(x) = x^x` is minimum at x=...... A) e B) -e C) 1/e D) -1/e

A

e

B

-e

C

1/e

D

-1/e

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Applications of Derivatives

    CHETANA PUBLICATION|Exercise Exercise|144 Videos

  • APPLICATION OF DEFINITE INTEGRATION

    CHETANA PUBLICATION|Exercise EXERCISE|80 Videos

  • BINOMIAL DISTRIBUTION

    CHETANA PUBLICATION|Exercise EXERCISE|108 Videos

Similar Questions

Explore conceptually related problems

If the function f(x) =log x, x in (1, e) , satisfies all the conditions of LMVT, then the value of c is..... A) 1 B) e C) 1/e D) e-1

The function f defined by f(x)=(x+2)e^(-x) is

The function f :R to R defined by f (x) = e ^(x) is

For the function f(x)=e^cosx , Rolle's theorem is

\int_{0}^log 5 frac{e^x sqrt (e^x -1)}{e^x + 3} dx=........... A) 3+2 pi B) 4- pi C) 2+ pi D) 4+ pi

If the function f(x)=x^(3)+e^(x//2)andg(x)=f^(-1)(x) , then the value of g'(1) is

The function f(x)=(ln(pi+x))/(ln(e+x)) is a)increasing in (0,oo) b)decreasing in (0,oo) c)Decreasing on [0,pi/e) and increasing on [pi/e,infty) d)Increasing on [0,pi/e) and decreasing on [pi/e,infty)

If x= e^2log_(e)(sin theta), y= e^2log_(e)(cos theta) , then dy/dx at theta=pi/4 ........... A) 1 B) -1 C) 0 D) 2

For the function f(x)=e^x,a=0,b=1 , the value of c in mean value theorem will be

CHETANA PUBLICATION-Applications of Derivatives-Exercise
  1. If the sum of the two numbers is 15 and the sum of their squares is mi...

    Text Solution

    |

  2. Two numbers x and y such that x + y=2 and x^3y is maximum, are...... A...

    Text Solution

    |

  3. A closed right circular cylinder of given total surface area, has maxi...

    Text Solution

    |

  4. The function f(x) = x^x is minimum at x=...... A) e B) -e C) 1/e D)...

    Text Solution

    |

  5. The equation of tangent to the curve y=x^2 +4x+ 1 at (-1, 1) is...... ...

    Text Solution

    |

  6. Function f(x) = 2x^3-3x^2-12x +2 has minimum at the point…………

    Text Solution

    |

  7. Find the approximate value of (4.01)^3

    Text Solution

    |

  8. Show that the function f(x)= x^3+10x +7 is increasing for all x in R.

    Text Solution

    |

  9. A particle moves according to the law s=t^3-6t^2+9t+ 15. Find the velo...

    Text Solution

    |

  10. Divide the number 20 into two parts such that their product is maximum...

    Text Solution

    |

  11. Find the equation of tangent to the curve at point sqrt x-sqrt y =1 at...

    Text Solution

    |

  12. The length x of a rectangle is increasing at the rate of 3 m/sec and t...

    Text Solution

    |

  13. Find the value of x such that f(x)=x^4-2x^3+1 is decreasing function.

    Text Solution

    |

  14. Check the applicability of Rolle's theorem for f(x) = (x-1) (2x-3), x ...

    Text Solution

    |

  15. The displacement x of a particle at time tis given by x= 160t-16t^2. S...

    Text Solution

    |

  16. If V denotes the volume and S denotes the surface area of a sphere the...

    Text Solution

    |

  17. Find the approximate value of e^1.002 given that e =2.7183.

    Text Solution

    |

  18. If the line y=4x-5 touches the curve y^2 = ax^3+b at point (2, 3) then...

    Text Solution

    |

  19. An aeroplane at an altitude of 1km is flying horizontally at 800 km/hr...

    Text Solution

    |

  20. Two sides of triangle are given, find the angle between them such that...

    Text Solution

    |