Home
Class 12
MATHS
Discuss the applicability of Rolles theo...

Discuss the applicability of Rolles theorem for the following functions on the indicated intervals:
`f(x)=|x|in[-1,1]`
`f(x)=3+(x-2)^(2//3)` in [1,3]
`f(x)=tanx in [0,pi]`
`f(x)=log{(x^2+a b)/(x(a+b))}` in [a,b], where 0 less than a less than b

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise ILLUSTRATION|2 Videos

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise SOLVED EXAMPLES|1 Videos

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise JEE Previous Year|9 Videos

  • 3D COORDINATION SYSTEM

    CENGAGE|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|17 Videos

Similar Questions

Explore conceptually related problems

Explain why Rolle's theorem is not applicable to the following functions in the respective intervals. f(x)=|1/x|,x in[-1,1]

Explain why Rolle's theorem is not applicable to the following functions in the respective intervals. f(x)=tanx,x in[0,pi]

Explain why Lagrange's mean value theorem is not applicable to the following functions in the respective intervals : f(x)=|3x+1|,x in[-1,3]

Explain why Lagrange's mean value theorem is not applicable to the following functions in the respective intervals: f(x) = (x +1)/(x), x in [-1,2]

Verify Rolle's theorem for the following f(x) = x^(3) -3x + 3 " in " 0 le x le 1

Explain why Lagrange's mean value theorem is not applicable to the following functions in the respective intervals : f(x)=(x+1)/x,x in[-1,2]

Prove that the function are increasing for the given intervals: f(x)=sinx+tanx-2x ,x in (0,pi/2)

Compute the value of 'c' satisfied by the Rolle's theorem for the function . f(x) = log ((x^(2) + 6)/(5x)) in the interval [2,3].

CENGAGE-APPLICATION OF DERIVATIVES-Examples
  1. Find approximate value of f (5.001) where f(x) =x^3-7x^2+15 .

    Text Solution

    |

  2. Find the approximate change in the volume V of a cube of side x meters...

    Text Solution

    |

  3. Discuss the applicability of Rolles theorem for the following functi...

    Text Solution

    |

  4. If the function f(x)=x^3-6x^2+a x+b defined on [1,3] satisfies Rolles ...

    Text Solution

    |

  5. How many roots of the equation (x-1)(x-2)(x-3)+(x-1)(x-2)(x-4) +(x-2)(...

    Text Solution

    |

  6. If 2a+3b+6c = 0, then show that the equation a x^2 + bx + c = 0 has at...

    Text Solution

    |

  7. Let f(x) be differentiable function and g(x) be twice differentiable f...

    Text Solution

    |

  8. Let f(x) be differentiable function and g(x) be twice differentiable f...

    Text Solution

    |

  9. If f : [-5, 5] to R is a differentiable function function and if f'(x)...

    Text Solution

    |

  10. Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 fo...

    Text Solution

    |

  11. Let f:[2,7]vec[0,oo) be a continuous and differentiable function. Then...

    Text Solution

    |

  12. Let f(x)a n dg(x) be differentiable function in (a , b), continuous at...

    Text Solution

    |

  13. Using Lagranges mean value theorem, prove that |cosa-cosb|<|a-b|dot

    Text Solution

    |

  14. Let f(x)a n dg(x) be two differentiable functions in Ra n df(2)=8,g(2)...

    Text Solution

    |

  15. Suppose alpha,betaa n dtheta are angles satisfying 0<alpha<theta<bet...

    Text Solution

    |

  16. Let f be continuous on [a , b],a >0,a n d differentiable on (a , b)dot...

    Text Solution

    |

  17. Prove that the equation of the normal to x^(2/3)+y^(2/3)=a^(2/3) is yc...

    Text Solution

    |

  18. If the area of the triangle included between the axes and any tangent ...

    Text Solution

    |

  19. Show that the segment of the tangent to the curve y=a/2I n((a+sqrt(a^2...

    Text Solution

    |

  20. If the tangent at (x1,y1) to the curve x^3+y^3=a^3 meets the curve aga...

    Text Solution

    |