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Calculus of Powers

Review question

Can we find the area inside a parabola, a tangent, and the $x$-axis?
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Ref: R6584

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Question

A plot of the curve $y = x^2$ with the point $P = (4,16)$. The tangent to the curve at $P$ intersects the $x$-axis at $Q$. The area bounded by the curve, the $x$-axis, and the tangent is labelled.

The figure shows part of the curve \(y = x^2\). \(PQ\) is the tangent to this curve at \(P\).

Calculate

the coordinates of \(Q\),
the area of the shaded region.