Home
Class 12
MATHS
Rolle’s theorem is applicable in the int...

Rolle’s theorem is applicable in the interval [-2, 2] for the function

A

`f(x)=x^3`

B

`f(x)=4x^4`

C

`f(x)=2x^3+3`

D

`f(x)=pi|x|`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    PATHFINDER|Exercise QUESTION BANK|23 Videos

Similar Questions

Explore conceptually related problems

The Rolle's theorem is applicable in the interval -1lexle1 for the function

The Rolle's thorem is applicable in the interval -1lexle1 for the function

Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? f(x)= [x]" for "x in [-2, 2] .

Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? f(x) = x^(2)-1 " for "x in [1, 2] .

Examine if Rolle's theorem is applicable to any of the following functions. Can you say some thing about the converse of Rolle's theorem from these example? f(x)= [x]" for "x in [5, 9] .

Consider the polynomial function f(x)=x^7/7-x^6/6+x^5/5-x^4/4+x^3/3-x^2/2+x Statement-1: The equation f(x) = 0 can not have two or more roots. Statement-2: Rolles theorem is not applicable for y=f(x) on any interval [a, b] where a,b in R

Examine whether Rolle's theorem is applicable to the following function in the given intervals: f(x) = cos x in - pi/2 le x le pi/2

Examine whether Rolle's theorem is applicable to the following functions in the given intervals : f(x)=cot x" in " -(pi)/(2) le x le (pi)/(2)

Examine whether Rolle's theorem is applicable to the following functions in the given intervals : f(x)=|x|" in " -1 le x le 1

Examine whether Rolle's theorem is applicable to the following functions in the given intervals : f(x)=1+(x-3)^((2)/(3))" in " 2 le x le 4

PATHFINDER-APPLICATION OF DERIVATIVE-QUESTION BANK
  1. If y=sec(tan^(-1)x), then value of dy/dx at x=1 is

    Text Solution

    |

  2. If f(x)=e^x(x-2)^2 then

    Text Solution

    |

  3. Let f(x)=sinx+2cos^2x,pi/4lexle(3pi)/4. then f attains its

    Text Solution

    |

  4. Let exp(x) denote exponential function e^x. If f(x)=exp(x^(1/x)).xgt0 ...

    Text Solution

    |

  5. The minimum value of the function f(x)=2|x-1|+|x-2| is

    Text Solution

    |

  6. Let f(x)={(x^2|cos"pi/x|,xne0),(0,x=0):}

    Text Solution

    |

  7. The function f:[0,3]rarr[1,29], defined by f(x)=2x^3-15x^2+36x+1 is

    Text Solution

    |

  8. if f(x)oversetxunderseto(int)e^(t^2)(t-2)(t-3)dt for all x in(0,oo), t...

    Text Solution

    |

  9. Let f:IRrarrIR be defined as f(x)=|x|+|x^2-1|.The total number of poin...

    Text Solution

    |

  10. Let p(x) be a real polynomial of least degree which has a local maximu...

    Text Solution

    |

  11. xx

    Text Solution

    |

  12. Let f(x)=(1-x)^2sin^2x+x^2 for all xinR and let g(x)=int1^x((2(t-1))/(...

    Text Solution

    |

  13. A spherical balloon is filled with 4500 pi cubic meters of helium gas....

    Text Solution

    |

  14. Let a, binR be such that the function f given by f(x)=ln|x|+bx^2+ax,xn...

    Text Solution

    |

  15. If f is a real-valued differentiable function such that f(x) f'(x)lt0 ...

    Text Solution

    |

  16. Rolle’s theorem is applicable in the interval [-2, 2] for the function

    Text Solution

    |

  17. Let y=((3^x-1)/(3^x+1))sinx+loge(2+x),xgt-1. Then at x=0 dy/dx equals

    Text Solution

    |

  18. Maximum value of the function f(x)=x/8+2/x on the interval [1,6] is

    Text Solution

    |

  19. For -pi/2ltxlt(3pi)/2, the value of d/dx{tan^(-1)"cosx/(1+sinx)} is eq...

    Text Solution

    |

  20. If f(x) and g(x) are twice differentiable functions on (0,3) satisfyin...

    Text Solution

    |