![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.](/calculus-of-powers/r6584/images/plot-labelled.png)
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 point \(Q\) is the \(x\)-intercept of the tangent. Can we find the equation of the tangent at P, and so find Q?
- the area of the shaded region.
Could we view this region as the difference of two simpler regions?