Home
Class 12
MATHS
In which of the following functions, Rol...

In which of the following functions, Rolle's theorem is applicable?

A

`f(x)=|x|i n-2lexle2`

B

`f(x)=tanx i n0lexlepi`

C

`f(x)=1+(x+2)^(2/3)i n1lexle3`

D

`f(x)=x(x-2)^2 i n 0lexle2`

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise EVALUATION TEST|20 Videos

  • APPLICATIONS OF DERIVATIVES

    TARGET PUBLICATION|Exercise CRITICAL THINKING|129 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

In which of the following function Rolle's theorem is applicable ?

In which of the following functions is Rolles theorem applicable? (a)f(x)={x ,0lt=x<1 0,x=1on[0,1] (b)f(x)={(sinx)/x ,-pilt=x<0 0,x=0on[-pi,0) (c)f(x)=(x^2-x-6)/(x-1)on[-2,3] (d)f(x)={(x^3-2x^2-5x+6)/(x-1)ifx!=1,-6ifx=1on[-2,3]

For which of the following functions is Rolle,s Theorem not applicable ?

For which of the following functions is Rolle s Theorem not applicable ?

Consider f(x)=|1-x| 1 lt=xlt=2 a n d g(x)=f(x)+bsinpi/2 x , 1 lt=xlt=2 Then which of the following is correct? Rolles theorem is applicable to both f, g a n d b = 3//2 LMVT is not applicable of f and Rolles theorem if applicable to g with b=1/2 LMVT is applicable to f and Rolles theorem is applicable to g with b = 1 Rolles theorem is not applicable to both f,g for any real b .

Consider a function f(x) = ln (x^2 + alpha)/7x . If for the given function, Rolle's theorem is applicable in [3,4] at a point C then find f'' (C)

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

Rolle’s theorem can not applicable for :

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

TARGET PUBLICATION-APPLICATIONS OF DERIVATIVES-COMPETITIVE THINKING
  1. If the Rolle's theorem for f(x)=e^(x)(sin x-cosx) is verified on [(pi)...

    Text Solution

    |

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

    Text Solution

    |

  3. In which of the following functions, Rolle's theorem is applicable?

    Text Solution

    |

  4. For the function f(x)=e^x,a=0,b=1, the value of c in mean value theore...

    Text Solution

    |

  5. The value of c in mean value theorem for the function f(x)=x^2 in [2,4...

    Text Solution

    |

  6. In the Mean value theorem f(b)-f(a)=(b-a)f'(c), if a=4, b=9 and f(...

    Text Solution

    |

  7. For the function f(x)=(x-1)(x-2) defined on [0,1/2], the value of 'c' ...

    Text Solution

    |

  8. The constant 'c' of Lagrange's mean value theorem of the function f(x)...

    Text Solution

    |

  9. If f(x)=cosx,0lexle(pi)/2 then the real number c of the mean value the...

    Text Solution

    |

  10. Let f(x) be continous on [0,6] and differentable on (0,6) Let f(0)=12 ...

    Text Solution

    |

  11. In [0, 1] Lagrange's mean value theorem is not applicable to

    Text Solution

    |

  12. The abscisssa of the points of the curve y=x^3 in the interval [-2,2],...

    Text Solution

    |

  13. If the function f(x) = x^(3) – 6ax^(2) + 5x satisfies the conditions o...

    Text Solution

    |

  14. For all real values of x, increasing function f(x) is

    Text Solution

    |

  15. The function f(x)=ax+b is strictly increasing for all real x is

    Text Solution

    |

  16. For Which value of x, the function f(x)=x^2-2x is decresing?

    Text Solution

    |

  17. The function f(x)= tan x - x

    Text Solution

    |

  18. f(x)={(0,x≤0),(x-3,xgt0):} The function f(x) is

    Text Solution

    |

  19. The function f(x)=cos x -2 px is monotonically decreasing for

    Text Solution

    |

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

    Text Solution

    |