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Calculus meets Functions

Review question

What's the area enclosed by $y=x(x-3)^2$ and a tangent?
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Ref: R7386

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Question

Show that the gradient of the curve \(y=x(x-3)^2\) is zero at the point \(P(1,4)\), and sketch the curve.

The tangent at \(P\) cuts the curve again at \(Q\). Calculate the area between the chord \(PQ\) and the curve.