Home
Class 12
MATHS
If the function f(x) =log x, x in (1, e)...

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

A

1

B

e

C

1/e

D

e-1

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)= e^x(sinx-cosx), x in [(pi)/4, (5pi)/4] satisfies all the conditions of the Rolle's theorem, then the value of c is...... A) 0 B) pi C) pi/2 D) pi/4

The function f(x) = x(x+3) e^(-x/2) satisfies all the conditions of Rolle's theorem on (-3,0) . Find the value of c such that f'(c) = 0

If f(x) = {((log_(e )x)/(x-1), ",", x != 1),(k, ",", x = 1):} is continuous at x = 1, then the value of k is

For the function f(x) = (log_(e )(1+x)-log_(e )(1-x))/(x) to be continuous at x = 0, the value of f(0) should be

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

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

If the function f(x)=((e^(kx)-1)tankx)/(4x^(2)), x ne 0 =16 , x=0 is continuous at x=0, then k= . . .a) 2 b) -2 c) pm8 d) 3

If a<0, the function f(x)=e^(ax)+e^(-ax) is a monotonically decreasing function for values of x given by

CHETANA PUBLICATION-Applications of Derivatives-Exercise
  1. Find the approximate value of log(10)(998), Given that log(10)(e) = 0....

    Text Solution

    |

  2. If the function f(x)= e^x(sinx-cosx), x in [(pi)/4, (5pi)/4] satisfies...

    Text Solution

    |

  3. If the function f(x) =log x, x in (1, e), satisfies all the conditions...

    Text Solution

    |

  4. The values of x for which f(x)= 2x^3-15x^2+ 36x+5 is decreasing, are.....

    Text Solution

    |

  5. If f(x) = x-sqrt x is increasing in the interval..

    Text Solution

    |

  6. The function f(x) = x- cosx, is increasing in....... A) (pi/2, pi) B)...

    Text Solution

    |

  7. The function f(x) =x^3-3x^2+3x-100, x in R is....... A) increasing B)...

    Text Solution

    |

  8. At x=-1, the function f(x) = 2x^3-3x^2-12x+12 is...... A) maximum B) m...

    Text Solution

    |

  9. Function f(x) = x^2-3x+4 has minimum value at..... A) x= 0 B) x= -3/...

    Text Solution

    |

  10. If the sum of the two numbers is 15 and the sum of their squares is mi...

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |

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

    Text Solution

    |