Question

Each side of a square is increasing at a rate of 6 cm/s. At what rate is the area of the square increasing when the area of the square is 16 cm^2?

Answer 1

\[A_\square = s^2\]
where s is the length of a side.

\[ds/dt = 6 cm/s\]
take the derivitive of the area
\[dA/dt = 2 *s *ds/dt\]
we are given that area is 16, so the length of a side (s) is 4
\[dA/dt = 2 *4 *6\]