Home
Class 12
MATHS
The tangent to the parabola y=x^2 has be...

The tangent to the parabola `y=x^2` has been drawn so that the abscissa `x_0` of the point of tangency belongs to the interval [1,2]. Find `x_0` for which the triangle bounded by the tangent, the axis of ordinates, and the straight line `y=x0 2` has the greatest area.

Promotional Banner

Topper's Solved these Questions

  • 3D COORDINATION SYSTEM

    CENGAGE PUBLICATION|Exercise DPP 3.1|11 Videos

  • APPLICATION OF INTEGRALS

    CENGAGE PUBLICATION|Exercise All Questions|143 Videos

Similar Questions

Explore conceptually related problems

The area of the region bounded by the parabola y=x^(2)-4x+5 and the straight line y=x+1 is-

A tangent is drawn to the parabola y^2=4 x at the point P whose abscissa lies in the interval (1, 4). The maximum possible area of the triangle formed by the tangent at P , the ordinates of the point P , and the x-axis is equal to

Find the area bounded by the parabola y^2=9x and the straight line x-y+2=0

Find the area bounded by the parabola y=x^(2)-6x+10 and the straight lines x=6 and y=2.

Find the area bounded by the parabola y=x^2+1 and the straight line x+y=3.

The area bounded by the parabolas y=4x^(2), y=(x^(2))/(9) and the straight line y = 2 is

The area bounded between the parabolas x^(2)=(y)/(4) and x^(2)=9y and the straight line y=2 is-

Find the area in the 1st quadrant, bounded by the parabola y=x^(2) , the straight line y=4 and the y-axis.

A tangent to the parabola y^2=8x makes an angle of 45^0 with the straight line y=3x+5. Then find one of the points of contact.

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. L L ' is the latus rectum of the parabola y^2= 4ax and PP' is a doubl...

    Text Solution

    |

  2. Let f(x0 be a non-constant thrice differentiable function defined on (...

    Text Solution

    |

  3. The tangent to the parabola y=x^2 has been drawn so that the abscissa ...

    Text Solution

    |

  4. Points on the curve f(x)=x/(1-x^2) where the tangent is inclined at an...

    Text Solution

    |

  5. The sum of the perimeter of a circle and square is k, where k is so...

    Text Solution

    |

  6. Separate the intervals of monotonocity for the function f(x)=x^2e^(-x)

    Text Solution

    |

  7. If f is a continuous function on [0,1], differentiable in (0, 1) such ...

    Text Solution

    |

  8. Separate the intervals of monotonocity for the function f(x)=-2x^3-9x^...

    Text Solution

    |

  9. Given g(x)=(x+2)/(x-1) and the line 3x+y-10=0. Then the line is tangen...

    Text Solution

    |

  10. Let g(x)=(f(x))^3-3(f(x))^2+4f(x)+5x+3sinx+4cosxAAx in Rdot Then prov...

    Text Solution

    |

  11. Let f be a continuous, differentiable, and bijective function. If the ...

    Text Solution

    |

  12. Find the intervals of decrease and increase for the function f(x)=cos(...

    Text Solution

    |

  13. If f(x)a n dg(x) are differentiable functions for 0lt=xlt=1 such that ...

    Text Solution

    |

  14. Find the interval of monotonocity of the function f(x)=|x-1|/x^2dot

    Text Solution

    |

  15. A continuous and differentiable function y=f(x) is such that its graph...

    Text Solution

    |

  16. Find the intervals in which the function f given by f(x)=(4sinx-2x-xc...

    Text Solution

    |

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

    Text Solution

    |

  18. Prove that the following functions are strictly increasing: f(x)=cot^(...

    Text Solution

    |

  19. The radius of the base of a cone is increasing at the rate of 3 cm/min...

    Text Solution

    |

  20. Find number of roots of f(x) where f(x) = 1/(x+1)^3 -3x + sin x

    Text Solution

    |