Home
Class 12
MATHS
If f(x) = x^(a) log x and f(0) = 0 then...

If `f(x) = x^(a) log x and f(0) = 0 ` then the value of `alpha` for which Rolle's theorem can be applied in [0,1] is

A

`-1/2`

B

`-1/3`

C

`-1/4`

D

`-1`

Text Solution

Verified by Experts

The correct Answer is:
B, C
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (COMPREHENSION TYPE PROBLEMS)|16 Videos
  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (MATHCING TYPE PROBLEMS)|1 Videos
  • APPLICATION OF DERIVATIVES

    VIKAS GUPTA (BLACK BOOK)|Exercise EXERCISE (SUBJECTIVE TYPE PROBLEMS)|22 Videos
  • AREA UNDER CURVES

    VIKAS GUPTA (BLACK BOOK)|Exercise AXERCISE (SUBJECTIVE TYPE PROBLEMS)|8 Videos

Similar Questions

Explore conceptually related problems

If f(x)=log x and f(1)=0; show then f(x)=x(log x-1)+1

Find the value of c in Rolle's theorem for the function f (x) = cos 2x on [0,pi] is

If f'(x)=f(x)+int_(0)^(1)f(x)dx ,given f(0)=1 , then the value of f(log_(e)2) is

Values of c of Rolle's theorem for f(x)=sin x-sin 2x on [0,pi]

" If "f(x)=x^((1)/(log x))" ,then set of all possible values of "x" for which "f'(x)=0" is "

Find the value of c in Rolles theorem for the function f(x)=x^(3)3x in[sqrt(3),0]

If f(x) = 4^(sin x) satisfies the Rolle's theorem on [0, pi] , then the value of c in (0, pi) for which f'(c ) = 0 is

If f(x)={(x^(alpha)logx , x > 0),(0, x=0):} and Rolle's theorem is applicable to f(x) for x in [0, 1] then alpha may equal to (A) -2 (B) -1 (C) 0 (D) 1/2

VIKAS GUPTA (BLACK BOOK)-APPLICATION OF DERIVATIVES -EXERCISE (ONE OR MORE THAN ANSWER IS/ARE CORRECT )
  1. The function f (x) =1+ x ln (x+ sqrt(1+ x ^(2)))-sqrt(1- x^(2)) is:

    Text Solution

    |

  2. Let m and n bwe positive integers and x,y gt 0 and x+y =k, where k is ...

    Text Solution

    |

  3. Determine the equation of straight line which is tangent at one point ...

    Text Solution

    |

  4. A curve is such that the ratio of the subnomal at any point to the sum...

    Text Solution

    |

  5. Number of A parabola of the form y= ax^2 +bx+c with a>0 intersectio...

    Text Solution

    |

  6. Find the gradient of the line passing through the point (2,8) and touc...

    Text Solution

    |

  7. The equation x + cos x = a has exactly one positive root. Complete set...

    Text Solution

    |

  8. Given that f (x) is a non-constant linear function. Then the curves :

    Text Solution

    |

  9. f (x) = int (0) ^(x) e ^(t ^(3)) (t ^(2) -1) (t+1) ^(2011) dt (x gt ...

    Text Solution

    |

  10. Let f(x)=sinx+a x+bdot Then which of the following is/are true? f(x)=0...

    Text Solution

    |

  11. Which of the following graphs represent function whose derivatives hav...

    Text Solution

    |

  12. Consider f (x)= sin ^(5) x-1, x in [0, (pi)/(2)], which of the followi...

    Text Solution

    |

  13. If f(x) = x^(a) log x and f(0) = 0 then the value of alpha for which ...

    Text Solution

    |

  14. Which of the following is/are true for the function f(x)= int (0) ^(x)...

    Text Solution

    |

  15. Let F (x) = (f (x ))^(2) + (f' (x ))^(2), F (0) =6, whtere f (x) is a ...

    Text Solution

    |

  16. Let f(x) = {{:( x^(3) + x^(2) - 10 x ,, -1 le x lt 0) , (sin x ,, 0 le...

    Text Solution

    |

  17. Minimum distnace between the curves y ^(2) =x-1and x ^(2) =x-1 and x ^...

    Text Solution

    |

  18. For the equation (e^-x)/(x+1) which of the following statement(s) is/a...

    Text Solution

    |

  19. If y = m x +5 is a tangent to the curve x ^(3) y ^(3) = ax ^(3) +by^(...

    Text Solution

    |

  20. If (f(x)-1) (x ^(2) + x+1)^(2) -(f (x)+1) (x^(4) +x ^(2) +1) =0 AA x...

    Text Solution

    |