Past exam of the mathematics course of the year 1 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / 9

Let $b_0=b(0)$ in centimetres and take $t$ in seconds. The constant rate gives $b(t)=b_0+4t$. By the Pythagorean theorem, the diagonal length isfor times when the side length is nonnegative. No initial value of $b$ is specified, so it must remain as a parameter. Choosing the time origin when $b=0$ gives the special convention $d(t)=\sqrt{100+16t^2}\mathrm{cm}$.

Differentiate before substituting the instantaneous side length. The related rates equation isAt the stated dimensions and rate,The diagonal grows more slowly than the changing side, since $b/d<1$.