Home
Class 12
MATHS
Let f(x)a n dg(x) be two differentiable ...

Let `f(x)a n dg(x)` be two differentiable functions in `Ra n df(2)=8,g(2)=0,f(4)=10 ,a n dg(4)=8.` Then prove that `g^(prime)(x)=4f^(prime)(x)` for at least one `x in (2,4)dot`

Promotional Banner

Topper's Solved these Questions

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise Exercise 5.1|11 Videos

  • APPLICATION OF DERIVATIVES

    CENGAGE|Exercise Exercise 5.2|6 Videos

  • 3D COORDINATION SYSTEM

    CENGAGE|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE|Exercise Solved Examples And Exercises|137 Videos

Similar Questions

Explore conceptually related problems

Let f(x) and g(x) be two differentiable functions in R and f(2)=8,g(2)=0,f(4)=10, and g(4)=8 Then prove that g'(x)=4f'(x) for at least one x in(2,4).

Let f(x)and g(x) be twice differentiable functions on [0,2] satisfying f''(x)=g''(x) , f'(1)=4 , g'(1)=6 , f(2)=3 and g(2)=9 . Then what is f(x)-g(x) at x=4 equal to ?

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

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

If f(x) and g(x) are differentiable functions for 0<=x<=1 such that f(0)=10,g(0)=2,f(1)=2,g(1)=4 then in the interval (0,1).f'(x)=0 for all xf'(x)+4g'(x)=0 for at least one xf(x)=2g'(x) for at most one x none of these

LEt f(x) be a differentiable function and f'(4)=5. Then,lim_(x rarr2)(f(4)-f(x^(2)))/(x-2) equals

If f(x),g(x) be twice differentiable functions on [0,2] satisfying f''(x)=g''(x)f'(1)=2g'(1)=4 and f(2)=3g(2)=9 then f(x)-g(x) at x=4 equals (A) 0 (B) 10 (C) 8 (D) 2

CENGAGE-APPLICATION OF DERIVATIVES-Solved Examples And Exercises
  1. Let f(x)a n dg(x) be two differentiable functions in Ra n df(2)=8,g(2)...

    Text Solution

    |

  2. The two curves x^3-3xy^2+2=0 and 3x^2y-y^3-2=0

    Text Solution

    |

  3. Find the angle of intersection of y=a^xa n dy=b^x

    Text Solution

    |

  4. If the sub-normal at any point on y=a^(1-n)x^n is of constant length,...

    Text Solution

    |

  5. Find the cosine of the angle of intersection of curves f(x)=2^x(log)e ...

    Text Solution

    |

  6. Find the value of a if the curves (x^2)/(a^2)+(y^2)/4=1a n dy^3=16 x c...

    Text Solution

    |

  7. The acute angle between the curves y= |x^2 -1| and y=|x^2- 3| at their...

    Text Solution

    |

  8. In the curve x^(m+n)=a^(m-n)y^(2n) , prove that the m t h power of the...

    Text Solution

    |

  9. Find the length of the tangent for the curve y=x^3+3x^2+4x-1 at point ...

    Text Solution

    |

  10. For the curve y=a1n(x^2-a^2) , show that the sum of length of tangent ...

    Text Solution

    |

  11. For the curve y=f(x) prove that (lenght n or mal)^2/(lenght or tanght...

    Text Solution

    |

  12. Find the condition if the equation 3x^2+4a x+b=0 has at least one root...

    Text Solution

    |

  13. Find c of Lagranges mean value theorem for the function f(x)=3x^2+5x+7...

    Text Solution

    |

  14. Let 0<a<b<pi/2dotIff(x)=|tanxtanatanbsinxsinasinbcosxcosacosb|,t h e n...

    Text Solution

    |

  15. Let f(x)a n dg(x) be differentiable for 0lt=xlt=2 such that f(0)=2,g(0...

    Text Solution

    |

  16. Prove that if 2a0 2<15 a , all roots of x^5-a0x^4+3a x^3+b x^2+c x+d=0...

    Text Solution

    |

  17. If f(x) is continuous in [a , b] and differentiable in (a,b), then pro...

    Text Solution

    |

  18. Prove that |tan^(-1)x-tan^(-1)y|lt=|x-y|AAx , y in Rdot

    Text Solution

    |

  19. Using Lagranges mean value theorem, prove that (b-a)/bltlog(b/a)lt(b-a...

    Text Solution

    |

  20. If a &gt; b &gt;0, with the aid of Lagranges mean value theorem, prov...

    Text Solution

    |

  21. Let f(x)a n dg(x) be two functions which are defined and differentiabl...

    Text Solution

    |