Home
Class 12
MATHS
If f and 'g' are differentiable function...

If f and 'g' are differentiable functions in [0, 1] satisfying f(0) = 2 = g(1), g(0) = 0 and f(1) = 6, then for some c `in` [0,1]:

A

2f(c ) = g(c )

B

2f(c )=3g(c )

C

f(c )=g(c )

D

f(c ) =2g (C )

Text Solution

Verified by Experts

The correct Answer is:
D
Promotional Banner

Topper's Solved these Questions

  • MEAN VALUE THEOREMS

    AAKASH SERIES|Exercise EXERCISE|28 Videos

  • MATHEMATICAL REASONING

    AAKASH SERIES|Exercise Practice Exercise|21 Videos

  • MEASURES OF DISPERSION (STATISTICS)

    AAKASH SERIES|Exercise Practice Exercise|54 Videos

Similar Questions

Explore conceptually related problems

If f and g are differentiable functions in [0,1] satifying f(0)=2=g(1),g(0)=0 and f(1) =6 , then for some c in (0,1)

Let f(x) and g(x) be differentiable functions for 0 le x le 1 such that f(0) = 2, g(0) = 0, f(1) = 6 . Let there exist a real number c in (0,1) such that f ’(c) = 2 g ’(c), then g(1) =

Let f and g be two diffrentiable functions on R such that f'(x) gt 0 and g'(x) lt 0 for all x in R . Then for all x

f(x) and g(x) are two differentiable functions on [0,2], such that f^('')(x) - g^('') (x) = 0,f' (1) = 4,g'(1) = 2, f(2) = 9, g(2) = 3, then f(x) = g(x) at x = 3//2 is

Let f(x) be continuous on [0, 6] and differentiable on (0, 6). Let f(0) = 12 and f(6) = -4 . If g(x)=(f(x))/(x+1) , then for some Lagrange's constant c in (0,6),g'( c )=

If f(x) and g(x) are continuous functions on the interval [0, 4] satisfying f(x)=f(4-x) and g(x)+g(4-x)=3 and int_(0)^(4) f(x)dx=2 then int_(0)^(4) f(x)g(x)dx=

AAKASH SERIES-MEAN VALUE THEOREMS-EXERCISE
  1. If f(x) = x^(3) + bx^(2) + ax satisfies the conditions of Rolle's the...

    Text Solution

    |

  2. If a + b + c = 0, then the equation 3ax^(2) + 2bx + c = 0 has, in the ...

    Text Solution

    |

  3. If 27a+9b+3c+d=0, then the equation 4ax^(3)+3bx^(2)+2cx+d =0 has atlea...

    Text Solution

    |

  4. Rolle's theorem cannot be applicable for

    Text Solution

    |

  5. The value of 'c' in Lagrange's thorem for f(x) = lx^(2) + mx + n [l ne...

    Text Solution

    |

  6. If f'(x) = (1)/(1+x^(2)) for all x and f(0) = 0, then:

    Text Solution

    |

  7. Let f be a function which is continuous and differentiable for all rea...

    Text Solution

    |

  8. In [0,1], Lagrange's mean value theorem is not applicable to (a) f(...

    Text Solution

    |

  9. Let f(x) and g(x) be differentiable functions for 0 le x le 1 such t...

    Text Solution

    |

  10. The value of 'a' for which x^(3) -3x +a=0 has two distinct roots in [...

    Text Solution

    |

  11. Let R rarr R be a continuous function define by f(x ) =(1)/(e^(x)+2e) ...

    Text Solution

    |

  12. The real number k for which the equation, 2x^(3)+3x+k=0 has two distin...

    Text Solution

    |

  13. If f and 'g' are differentiable functions in [0, 1] satisfying f(0) = ...

    Text Solution

    |

  14. If the Rolle's theorem holds for the function f(x) = 2x^(3) + ax^(2) +...

    Text Solution

    |

  15. Let f(1)= -2 and f'(x ) ge 4.2 for 1 le x le 6 . The possible value o...

    Text Solution

    |

  16. A value of c for which the conclusion of Mean Value Theorem holds for ...

    Text Solution

    |

  17. If 2a + 3b + 6c = 0, then atleast one root of the equation ax^(2) + bx...

    Text Solution

    |

  18. If the equation a(n)x^(n) + a(n-1) x^(n-1)+"......" + a(1) x= 0 (a(1...

    Text Solution

    |

  19. Let f be differentiable for all x. If f(1) = -2 and f'(x) ge 2 for...

    Text Solution

    |

  20. Consider the functions, f(x) = |x -2 | + |x - 5 |, x in R Statement-1...

    Text Solution

    |