Hence find the approximate increase in \(x\) which will cause \(y\) to increase from \(4\) to \(4.05\).

Suppose \(y = f(x)\), and that \((x,y)\) is on this curve. We now increase \(x\) by a small amount \(\delta x\), which increases \(y\) by a small amount \(\delta y\) (\(y\) could decrease, in which case \(\delta y\) would be negative).

Can you see why \(y'\) evaluated at \(x\) is roughly \(\dfrac{\delta y}{\delta x}\)? A diagram might help…