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

-2

B

-1

C

0

D

`1/2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise COMPETITIVE THINKING|161 Videos

  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise EVALUATION TEST|20 Videos

  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise EVALUATION TEST|20 Videos

  • APPICATIONS OF DEFINITE INTEGRAL

    TARGET PUBLICATION|Exercise EVALUATION TEST|18 Videos

  • BINOMIAL DISTRIBUTION

    TARGET PUBLICATION|Exercise EVALUTION TEST|12 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

TARGET PUBLICATION-APPLICATIONS OF DERIVATIVES-CRITICAL THINKING
  1. If the functio f(x)^(3)-6x^(2)+ax+b satisfies Rolle's theorem in the i...

    Text Solution

    |

  2. The function f(x)=x(x+3)e^(-(1/2)x) satisfies the conditions of Rolle'...

    Text Solution

    |

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

    Text Solution

    |

  4. The value of c in Lagrange's mean value theorem for the function f(...

    Text Solution

    |

  5. Varify Lagrange's mean value theorem for the function f(x)=x+(1)/(x)...

    Text Solution

    |

  6. From mean value theoren : f(b)-f(a)=(b-a)f^(prime)(x1); a lt x1 lt b...

    Text Solution

    |

  7. The value of c in (0,2) satisfying the Mean Value theorem for the func...

    Text Solution

    |

  8. In the Mean Value theorem (f(b)-f(a))/(b-a)=f'(c) if a=0 , b =1/2 a...

    Text Solution

    |

  9. IF f(x)=1-x^3-x^5 is decreasing for

    Text Solution

    |

  10. IF f(x)=2x^3+3x^2-12x+5 , then the interval in which (l1) increases an...

    Text Solution

    |

  11. The function f(x)=x/(1+|x|) is differentiable in:

    Text Solution

    |

  12. The values of x for which the function (logx)/x decreases is

    Text Solution

    |

  13. IF f(x)=1/(x+1)-log(1+x),xgt0 , then f is

    Text Solution

    |

  14. Let f(x)=x^3+3/2x^2+3x+3, then f(x) is

    Text Solution

    |

  15. The set of all points for which f(x)=x^(2)e^(-x) stricltly increasing ...

    Text Solution

    |

  16. If a<0, the function f(x)=e^(ax)+e^(-ax) is a monotonically decreasing...

    Text Solution

    |

  17. If f(x)= kx^3-9x^2+9x+3 is increasing on R then

    Text Solution

    |

  18. The function f(x)=(lambdasinx+2cosx)/(sinx+cosx) is increasing, if (a)...

    Text Solution

    |

  19. The function which is neither decreasing nor increasing in (pi/2,(3pi)...

    Text Solution

    |

  20. The function f(x)= x +1/x (x != 0) is a non-increasing function in the...

    Text Solution

    |