Home
Class 12
MATHS
If f'[x) exists for all points i...

If f'[x) exists for all points in [a,b] and `(f(c ) -f(a))/(c-a) =(f(b)-f( c))/(b-c)` where `a lt c lt b`, then there is a number l such that `a lt l lt b` and `f''(l)=0`

Promotional Banner

Topper's Solved these Questions

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise PROBLEM SET (4)|20 Videos

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise PROBLEM SET (5) (MULTIPLE CHOICE QUESTIONS) |12 Videos

  • LIMITS, CONTINUITY AND DIFFERENTIABILITY

    ML KHANNA|Exercise PROBLEM SET (2) (FILL IN THE BLANKS) |2 Videos

  • INVERSE CIRCULAR FUNCTIONS

    ML KHANNA|Exercise Self Assessment Test|25 Videos

  • LINEAR PROGRAMMING

    ML KHANNA|Exercise Self Assessment Test|8 Videos

Similar Questions

Explore conceptually related problems

If f'(c)=(f (b)-f(a))/(b-a) , where f(x) =e^(x), a=0 and b=1 , then: c = ….

Let f(x) is differentiable function in [2, 5] such that f(2)=(1)/(5) and f(5)=(1)/(2) , then the exists a number c, 2 lt c lt 5 for which f '(c) equals :-

If a lt b lt c lt d lt e and f(x) =(x-a)^(2) (x-b) (x -c) (x-d) (x-e ) which of the following is true?

If f(x) = x (1 - log x), " where " x gt 0 , show that (a -b) log c = b (1 - logb) - a(1 - log a), " where " 0 lt a lt c lt b

Let f: (0,1) to R be defined by f(x)=(b-x)/(1-bx) where b is a constant such that 0 lt b lt 1 Then:

f(x) and g(x) are differentiable functions for 0 le x le 2 such that f(0)=5, g(0)=0, f(2)=8, g(2)=1 . Show that there exists a number c satisfying 0 lt c lt 2 and f'(c)=3g'(c) .

If 0lt a lt b lt (pi)/(2) and f(a,b) =(tan b- tana)/(b-a) then,

ML KHANNA-LIMITS, CONTINUITY AND DIFFERENTIABILITY -PROBLEM SET (3)
  1. Verify Rolle's theorem for the following function f(x) = 2x^(3) + x^(2...

    Text Solution

    |

  2. Verify Rolles theorem for the function: f(x)=x(x+3)e^(-x//2) on [-3...

    Text Solution

    |

  3. Show that there is no real number p for which the equation x^2 -3x + p...

    Text Solution

    |

  4. Verify Rolle's theorem for the function f(x) = x^(2) in the interval [...

    Text Solution

    |

  5. Verify the Rolle's theorem for the functionf(x) = x^(2) - 3x+2 ...

    Text Solution

    |

  6. If a+b + c = 0, then show that the quadratic equation 3ax^(2) + 2bx +c...

    Text Solution

    |

  7. Discuss the applicability of Rolles theorem for the function f(x)=x...

    Text Solution

    |

  8. Discuss the applicability of Rolle's theorem on the function given by ...

    Text Solution

    |

  9. Discuss the application of Rolle's theorem to the function f(x) = log ...

    Text Solution

    |

  10. Verify Rolle's theorem for the function f(x) = x^(3) -6x^(2) + 11x-6 i...

    Text Solution

    |

  11. Verify Rolle's Theorem for the function f(x)= 10x - x^(...

    Text Solution

    |

  12. Find 'c' of the mean value theorem, if: f(x) = x(x-1) (x-2), a=0, b=...

    Text Solution

    |

  13. If f(x) =log x find all numbers strictly between e^(2) and e^(3) such ...

    Text Solution

    |

  14. Separate the intervals in which the polynomial 2x^(3) -15x^(2) + 36x+1...

    Text Solution

    |

  15. Use the function f(x)=x^(1/x),x >0, to determine the bigger of the two...

    Text Solution

    |

  16. Show that Lagrange's mean value theorem does not holdior the function ...

    Text Solution

    |

  17. Verify Lagrange's mean yalue'theorem for the function f(x) = sin x in ...

    Text Solution

    |

  18. If f'[x) exists for all points in [a,b] and (f(c ) -f(a))/(...

    Text Solution

    |

  19. If f(x) = (x-1)(x-2) and a = 0, b = 4, find 'c' using Lagrange's mean ...

    Text Solution

    |

  20. Examine if Mean Value Theorem applies to f(x) = x^(3) + 3x^(2) - 5x i...

    Text Solution

    |