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

Let `f(x)a n dg(x)` be two functions which are defined and differentiable for all `xgeqx_0dot` If `f(x_0)=g(x_0)a n df^(prime)(x)>g^(prime)(x)` for all `x > x_0,` then prove that `f(x)>g(x)` for all `x > x_0dot`

A

`f(x) lt g(x)` for some `x gt x_(0)`

B

`f(x)=g(x)` for some `x gt x_(0)`

C

`f(x) gt g(x)` only for some `xgt x_(0)`

D

`f(x) gt g(x)` for all `xgt x_(0)`

Text Solution

Verified by Experts

The correct Answer is:
B
Promotional Banner

Topper's Solved these Questions

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise Exercise (More Than One Correct Option Type Questions)|15 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Statement I And Ii Type Questions)|7 Videos

  • DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 6|4 Videos

  • DIFFERENTIATION

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 10|4 Videos

  • ELLIPSE

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|27 Videos

Similar Questions

Explore conceptually related problems

If f(x)a n dg(x) be two function which are defined and differentiable for all xgeqx_0dot If f(x_0)=g(x_0)a n df^(prime)(x)>g^(prime)(x) for all x> x_0, then prove that f(x)>g(x) for all x > x_0dot

Let fa n dg be differentiable on R and suppose f(0)=g(0)a n df^(prime)(x)lt=g^(prime)(x) for all xgeq0. Then show that f(x)lt=g(x) for all xgeq0.

Let fa n dg be differentiable on R and suppose f(0)=g(0)a n df^(prime)(x)lt=g^(prime)(x) for all xgeq0. Then show that f(x)lt=g(x) for all xgeq0.

Let f(x) and g(x) be defined and differntiable for all x ge x_0 and f(x_0)=g(x_0) f(x) ge (x) for x gt x_0 then

Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 for all x in [1,6], then find the range of values of f(6)dot

Let f be differentiable for all x , If f(1)=-2a n df^(prime)(x)geq2 for all x in [1,6], then find the range of values of f(b)dot

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

Let f(x)a n dg(x) be two differentiable functions in R a n d f(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

If f(x) = (a-x^n)^(1/n), a > 0 and n in N , then prove that f(f(x)) = x for all x.

Let f(x)a n dg(x) be two function having finite nonzero third-order derivatives f'''a n dg''' for all x in Rdot If f(x)g(x)=1 for all x in R , then prove that f'''(/)f^(prime)-g'''^(/)g^(prime)=3(f''^(/)f-g''^(/)g)dot

ARIHANT MATHS ENGLISH-DY / DX AS A RATE MEASURER AND TANGENTS, NORMALS -Exercise (Single Option Correct Type Questions)
  1. The graphs y=2x^(3)-4x+2and y=x^(3)+2x-1 intersect in exactly 3 distin...

    Text Solution

    |

  2. In which of the following functions is Rolles theorem applicable? (a)f...

    Text Solution

    |

  3. The figure shows a right triangle with its hypotenuse OB along the y-a...

    Text Solution

    |

  4. Number of positive integral value(s) of a for which the curve y=a^(x) ...

    Text Solution

    |

  5. Given f(x)=4-(1/2-x)^(2/3),g(x)={("tan"[x])/x ,x!=0 1,x=0 h(x)={x},k(...

    Text Solution

    |

  6. If the function f(x)=x^(4)+bx^(2)+8x+1 has a horizontal tangent and a...

    Text Solution

    |

  7. Coffee is coming out from a conical filter, with height and diameter b...

    Text Solution

    |

  8. A horse runs along a circle with a speed of 20k m//h . A lantern is at...

    Text Solution

    |

  9. Water runs into an inverted conical tent at the rate of 20 ft^3/ min a...

    Text Solution

    |

  10. Let f(x)=x^3-3x^2+2x Find f'(x)

    Text Solution

    |

  11. The x-intercept of the tangent at any arbitrary point of the curve a/(...

    Text Solution

    |

  12. If f(x) is continuous and differentible over [-2, 5] and -4lef'(x)le3 ...

    Text Solution

    |

  13. A curve is represented parametrically by the equations x=t+e^(at) and ...

    Text Solution

    |

  14. At any two points of the curve represented parametrically by x=a (2 co...

    Text Solution

    |

  15. Let F(x)=int(sinx)^(cosx)e^((1+sin^(-1)(t))dt on [0,(pi)/(2)], then

    Text Solution

    |

  16. Given f'(1)=1and f(2x)=f(x)AAxgt0.If f'(x) is differentiable, then th...

    Text Solution

    |

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

    Text Solution

    |

  18. The range of values of m for which the line y = mx and the curve y=(x)...

    Text Solution

    |

  19. Let S be a square with sides of length x. If we approximate the change...

    Text Solution

    |

  20. Consider f(x)=int1^x(t+1/t)dt and g(x)=f'(x) If P is a point on the cu...

    Text Solution

    |