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The tangent to the parabola {y}={x}^{{2}} has been drawn so th

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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 $y = x 02$ has the greatest area.

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Jack Discussed

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 = x 02

has the greatest area.

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Question Text

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 = x 02

has the greatest area.

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