Home
Class 12
MATHS
Let f(x) and g(x) be differentiable for...

Let f(x) and g(x) be differentiable for `0 le x le 1` such that `f(0)=0, g(0)=0, f(1)=6`. Let there exist a real number c in (0, 1) such that `f'(c )=2g'(c )`, then the value of g(1) must be :

A

1

B

3

C

-2

D

-1

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    MODERN PUBLICATION|Exercise Latest Questions from AIEEE/JEE Examinations|13 Videos
  • APPLICATION OF DERIVATIVES

    MODERN PUBLICATION|Exercise Recent Competitive Questions (Questions from Karnataka CET & COMED)|25 Videos
  • APPLICATION OF DERIVATIVES

    MODERN PUBLICATION|Exercise Recent Competitive Questions (Questions from Karnataka CET & COMED)|25 Videos
  • AREA UNDER CURVES

    MODERN PUBLICATION|Exercise Recent Competitive Questions (Question from karnataka CET & COMED)|9 Videos

Similar Questions

Explore conceptually related problems

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] :

Let f be a real valued function defined on (0, 1) cup (2, 4) , such that f(x)=0 , for every x, then :

Let f(x) have second derivative at c such that f'(c )=0 and f''(c ) gt 0 , then c is a point of :

If the function f(x)= x^(3)+e^(x/2) and g(x) = f^(-1)(x) then the value of g^(')(1) is

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)=x^2" and "g(x)=2x+1 be two real values functions, find (f+g)(x)

Let f(x)=x^2" and "g(x)=2x+1 be two real values functions, find (f-g)(x)

Let f:(-1,1)toR be a differentiable function with f(0)=-1 and f'(0)=1 . Let g(x)=[f(2f(x)+2)]^(2) . Then g'(0)=

MODERN PUBLICATION-APPLICATION OF DERIVATIVES -Multiple Choice Questions LEVEL-II
  1. The curves y=x^(2) and 6y=7-x^(3) intersect at the point (1, 1) at an ...

    Text Solution

    |

  2. The curve ((x)/(a))^(n)+((y)/(b))^(n)=2 touches the straight line (x)/...

    Text Solution

    |

  3. Let f(x) and g(x) be differentiable for 0 le x le 1 such that f(0)=0,...

    Text Solution

    |

  4. A cannon ball is fired at an angle theta, 0 lt theta lt pi//2, with th...

    Text Solution

    |

  5. The area of the triangle formed by the co-ordinate axes and a tangent ...

    Text Solution

    |

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

    Text Solution

    |

  7. Let f(x) be twice differentiable on [1, 3], and let f(1)=f(3). Further...

    Text Solution

    |

  8. Let f be a real valued function defined on (0, 1) cup (2, 4), such tha...

    Text Solution

    |

  9. If x in (0, pi//2), then :

    Text Solution

    |

  10. The curve y=ax^(3)+bx^(2)+cx is inclined at 45^(@) to X-axis at (0, 0)...

    Text Solution

    |

  11. If log(0.3) (x-1) lt log(0.09) (x-1), then x lies in the interval :

    Text Solution

    |

  12. The angle of intersection of the two curves xy=a^(2) and x^(2)-y^(2)=2...

    Text Solution

    |

  13. The length of subtangent to the curve x^(2)+xy+y^(2)=7 at (1, -3) is ...

    Text Solution

    |

  14. The equation 3x^(2)+4ax+b=0 has atleast one root in (0, 1) if :

    Text Solution

    |

  15. The curve y-e^(xy)+x=0 has a vertical tangent at the point :

    Text Solution

    |

  16. If the normal to the curve y = f(x) at the point (3, 4) makes an angle...

    Text Solution

    |

  17. If x+y=k is normal to y^(2)=12x, then k is :

    Text Solution

    |

  18. The two curves x^(3)-3xy^(2)+2=0 and 3x^(2)y-y^(3)-2=0:

    Text Solution

    |

  19. The greatest distance of the point P(10, 7) form the circle x^(2)+y^(...

    Text Solution

    |

  20. The greatest value of f(x)=(x+1)^(1//3)-(x-1)^(1//3) on [0, 1] is :

    Text Solution

    |