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

  • CONTINUITY AND DIFFERENTIABILITY

    BANSAL|Exercise All Questions|425 Videos

Similar Questions

Explore conceptually related problems

Find the area bounded by the line y=x , the x-axis and the ordinates x=-1 and x=2

Find the area of the region bounded by the line y=3x+2 , the x-axis and the ordinates x=-1 and x=1

Find the area of the region bounded by the line y=3x+2 ,the x-axis and the ordinates x=-1 and x=1

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

Find the area bounded by the curve y=xe^(x^(2)) x-axis and the ordinates x=0 and x=h.

Find the area of the triangle formed by the straight lines y=2x, x=0 and y=2 by integration.

A tangent is drawn to the parabola y^2=4a x at the point P whose abscissa lies in the interval (1, 4). The maximum possible area f the triangle formed by the tangent at P , the ordinates of the point P , and the x-axis is equal to 8 (b) 16 (c) 24 (d) 32

Find the equations of tangent to the curve x^(2)+y^(2)-4x13=0 at (1,4). Also find (1) area of the triangle formed by the tangent line and the co ordinate axes.

BANSAL-APPLICATION OF DERIVATIVE-All Questions
  1. Find two positive numbers x and y such that x+y=60\ a n d\ x^3y is max...

    Text Solution

    |

  2. Rectangles are inscribed inside a semi-circle of radius rdot Find the ...

    Text Solution

    |

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

    Text Solution

    |

  4. A sheet of area 40m^2 is used to make an open tank with square base. F...

    Text Solution

    |

  5. A right circular cylinder of maximum volume is inscribed in a given ri...

    Text Solution

    |

  6. Show that semi-vertical angle of right circular cone of given surfa...

    Text Solution

    |

  7. If the sum of the lengths of the hypotenuse and another side of a righ...

    Text Solution

    |

  8. Find the point (alpha,beta) on the ellipse 4x^2+3y^2=12 , in the first...

    Text Solution

    |

  9. A rectangle is inscribed in an equilateral triangle of side length 2a ...

    Text Solution

    |

  10. Tangents are drawn to x^2+y^2=16 from the point P(0, h)dot These tange...

    Text Solution

    |

  11. f(x)=x^(1/5) at x=0 has inflection point. y"\ DdotNdotEdot\ at x=0

    Text Solution

    |

  12. f(x)=x^3a t\ x=0 has inflection point y ' '=0 at x=0 and change sign.

    Text Solution

    |

  13. f(x)=|x^2-1| has no inflection point in its domain as no tangent ca...

    Text Solution

    |

  14. Number of points of inflection for f(x)=x^2e^(-|x|) is 1 (b) 2 (...

    Text Solution

    |

  15. Find the value of a if x^3-3x+a=0 has three distinct real roots.

    Text Solution

    |

  16. Prove that there exist exactly two non-similar isosceles triangles A B...

    Text Solution

    |

  17. Find the set of value of m for the cubic x^3-3/2x^2+5/2=(log)(1/4)(...

    Text Solution

    |

  18. The set of value(s) of a for which the function f(x)=(a x^3)/3+(a+2)x^...

    Text Solution

    |

  19. The number of values of k for which the equation x^3-3x+k=0 has two di...

    Text Solution

    |

  20. Find the shortest distance between the curves y^2=x^3a n d\ 9x^2+9y...

    Text Solution

    |