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

Let f (x) and g (x) be differentiable for 0 < x < 1 such 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) 2.5 D) -1

A

1

B

3

C

2.5

D

-1

Text Solution

Verified by Experts

Promotional Banner

Topper's Solved these Questions

  • Applications of Derivatives

    CHETANA PUBLICATION|Exercise Exercise|144 Videos

  • APPLICATION OF DEFINITE INTEGRATION

    CHETANA PUBLICATION|Exercise EXERCISE|80 Videos

  • BINOMIAL DISTRIBUTION

    CHETANA PUBLICATION|Exercise EXERCISE|108 Videos

Similar Questions

Explore conceptually related problems

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

Let f: R to R be a differentiable function . If f is even, then f'(0) is equal to

Let f(x) =x^(p) cos (1/x) , when x ne 0 and f(x)=0 , when x=0 . Then f(x) will be differentiable at x=0 , if

The function f(x)=x/(1+|x|) is differentiable in: a) x in R b) x=0 only c) xlt0 d) xgt0

If f(x) = {{:(-x, " when "x lt 0),(x^(2), " when "0 le x le 1),(x^(3) -x+1, " when " x gt 1):} then f is differentiable at

If f(x) = {{:( e^(x) +ax ,"for " x lt 0 ),( b(x-1) ^(2) ,"for " xge 0):}, is differentiable at x =0,then (a,b) is

Let f(x) be a function satisfying f'(x)=f(x) with f(0) =1 and g(x) be a function that satisfies f(x) + g(x) = x^2 . Then the value of the integral int_0^1f(x) g(x) dx , is

Let f(x) be continous on [0,6] and differentable 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)=

Let f : R to R be a function defined by f(x) = max. {x, x^(3)} . The set of all points where f(x) is NOT differentiable is

If the function f defined on R-{0} is a differentiable function and f(x^3)=x^5 for all x, then f'(27)=

CHETANA PUBLICATION-Applications of Derivatives-Exercise
  1. If f(x) = frac {x^2 -1}{x^2 +1}, for every real x, then the minimum v...

    Text Solution

    |

  2. A ladder 5 m in length is resting against vertical wall. The bottom of...

    Text Solution

    |

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

    Text Solution

    |

  4. Let f (x) = x^3-6x^2 +9x +18, then f(x) is strictly decreasing in- A) ...

    Text Solution

    |

  5. If x = -1 and x= 2 are the extreme points of y= alpha log x+ beta x^2...

    Text Solution

    |

  6. The normal to the curve x^2+2xy-3y^2= 0 at (1, 1)

    Text Solution

    |

  7. The equation of the tangent to the curve y=1-e^(x/2) at the point of ...

    Text Solution

    |

  8. If the tangent at (1, 1) on y^2=x (2-x)^2 meets the curve again at P t...

    Text Solution

    |

  9. The approximate value of tan (44^° 30') given that 1^° = 0.0175. A) 0...

    Text Solution

    |

  10. If normal to the curve y = f(x) is parallel to x-axis, then A) dy/dx=...

    Text Solution

    |

  11. The equation of tangent y= x^2 +4x+1 at (-1, 2) is………. A) 2x -y+4=0 B...

    Text Solution

    |

  12. The equation of tangent to the curve y =3x^2-x+ 1 at p (1, 3) is..... ...

    Text Solution

    |

  13. The equation of tangent to the curve y =3x^2-x+ 1 at p (1, 3) is..... ...

    Text Solution

    |

  14. If the curve y=ax^2-6x +b passes through (0,2) and its tangent at x =3...

    Text Solution

    |

  15. The equation of normal to the curve y^2 (2a-x) =x^3 at the point (a, -...

    Text Solution

    |

  16. The points of the curve 9y^2= x^3, where the normal to the curve makes...

    Text Solution

    |

  17. The co-ordinate of the point on the curve y = 6x - x^2, the tangent at...

    Text Solution

    |

  18. The co-ordinate of the point on the curve y= x logx at which the norma...

    Text Solution

    |

  19. If the tangent to the curve y=x (x-1) at the point (a, b) is parallel ...

    Text Solution

    |

  20. A particle moves according to the law s= t^3-6t^2+9t +5. The displacem...

    Text Solution

    |