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The slope of a curve art each of its poi...

The slope of a curve art each of its points is equal to the square of the abscissa of the point. Find the particular curve through the point (-1,1).

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Knowledge Check

  • If the slope of the tangent is equal to the square of tha abscissa of the point on the curve, then the differential equation is

    A
    `(dy)/(dx)=kx^(2)`
    B
    `(dy)/(dx)=x^(2)`
    C
    `(dx)/(dy)=kx^(2)`
    D
    `(dx)/(dy)=x^(2)`

  • The equation of the curve such that the subtangent at any point of the curve is two times the abscissa of the point and curve passes through point (1,2) is:

    A
    `y^(2) = x + 3`
    B
    `y = x^(2)`
    C
    `y^(2) = 4x`
    D
    `y = 2x^(2)`

  • At any point on a curve , the slope of the tangent is equal to the sum of abscissa and the product of ordinate and abscissa of that point.If the curve passes through (0,1), then the equation of the curve is

    A
    `y=2e^(x^2/2)-1`
    B
    `y=2e^(x^2/2)`
    C
    `y=e^(-x^2)`
    D
    `y=2e^(-x^2)-1`

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    The slope of the curve at any point is the reciprocal of twice the ordinate at the point. The curve also passes through the point (4,3). It is a parabola ......

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    If the slope of a curve at any point is the reciprocal of twice the ordinate at the point and it passes through the point (4, 3). Then, the equation of the curve is

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