Differentiation

A rectangle has fixed perimeter \(40\text{ cm}\). One side has length \(x\) cm and increases at \(1\text{ cm/s}\).

1. Express its area \(A\) in terms of \(x\).

2. Find \(\dfrac{\mathrm{d}A}{\mathrm{d}t}\) when \(x=6,\ 10,\ 14\).

3. Explain how \(\dfrac{\mathrm{d}A}{\mathrm{d}t}\) can be zero even though both side lengths are changing.