Home
Class 12
MATHS
Consider f(x)=int1^x(t+1/t)dt and g(x)=f...

Consider `f(x)=int_1^x(t+1/t)dt` and `g(x)=f'(x)` If P is a point on the curve `y=g(x)` such that the tangent to this curve at P is parallel to the chord joining the point `(1/2,g(1/2))` and `(3,g(3))` of the curve then the coordinates of the point P

A

can't be found out

B

`((7)/(4),(65)/(28))`

C

`(1, 2)`

D

`(sqrt((3)/(2)),(5)/(sqrt6))`

Text Solution

Verified by Experts

The correct Answer is:
D
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

Consider f(x) = int_(1)^(x)(t + 1t)dt and g(x) = f'(x) for x in [1/2, 3] .If P is a point on the curve y = g(x) such that the tangent to curve at P is parallel to a chord joining the points (1/2, g(1/2)) and (3,g(3)) of the curve, then if ordinate of point P is lambda then sqrt(6) lambda is equal to:

When the tangent the curve y=x log (x) is parallel to the chord joining the points (1,0) and (e,e) the value of x , is

Find a point on the curve y=x^2+x , where the tangent is parallel to the chord joining (0, 0) and (1, 2).

Find a point on the curve y=x^3-3x where the tangent is parallel to the chord joining (1,-2)a n d(2,2)dot

Find a point on the curve y=x^2+x , where the tangent is parallel to the chord joining (0,0) and (1,2).

Find a point on the curve y=x^3-3x where the tangent is parallel to the chord joining (1,\ -2) and (2,\ 2) .

Find a point on the curve y=(x-3)^2 , where the tangent is parallel to the line joining (4,\ 1) and (3,\ 0) .

Write the coordinates of the point at which the tangent to the curve y=2x^2-x+1 is parallel to the line y=3x+9 .

Show that the tangent to the curve 3x y^2-2x^2y=1a t(1,1) meets the curve again at the point (-(16)/5,-1/(20))dot

Show that the tangent to the curve 3x y^2-2x^2y=1a t(1,1) meets the curve again at the point (-(16)/5,-1/(20))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

    |