Answer
The rate of change of $S$ with respect to weight is $$\frac{\sqrt{20}}{40\sqrt w}$$
$S$ increases more rapidly with respect to weight at lower body weights.
Work Step by Step
$$S=\frac{1}{60}\sqrt{wh}$$
For $h=180cm$, we have $$S=\frac{1}{60}\sqrt{180w}$$
So the rate of change of $S$ with respect to weight is the derivative of $S$:
$$S'=\frac{\sqrt{180}}{60}(\sqrt w)'=\frac{\sqrt{180}}{60}(w^{1/2})'=\frac{\sqrt{180}}{60}\times\frac{1}{2}w^{-1/2}=\frac{\sqrt{180}}{120\sqrt w}$$ $$S'=\frac{3\sqrt{20}}{120\sqrt w}=\frac{\sqrt{20}}{40\sqrt w}$$
Since $w$ is in the denominator, this formula tells us that the rate of change for the body surface are is inversely proportional with the weight $w$.
Therefore, $S$ increases more rapidly with respect to weight at lower body weights.
