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 \(P\).


  1. the coordinates of \(Q\),

The point \(Q\) is the \(x\)-intercept of the tangent. Can we find the equation of the tangent at P, and so find Q?

  1. the area of the shaded region.

Could we view this region as the difference of two simpler regions?