Chapter 14.5, Problem 39E

(a)

To determine

To find: The rate of change of the volume of the box whose length $l$ increase from $1\text{m/s}\text{to}2\text{m/s}$, width $w$ increase from $\text{2}\text{m/s}\text{to}2\text{m/s}$ and height $h$ decrease from $2\text{m/s}\text{to}3\text{m/s}$.

(b)

To determine

To find: The rate of change of the surface of the box whose length $l$ increase from $1\text{m/s}\text{to}2\text{m/s}$, width $w$ increase from $\text{2}\text{m/s}\text{to}2\text{m/s}$ and height $h$ decrease from $2\text{m/s}\text{to}3\text{m/s}$.

(c)

To determine

To find: The rate of change of the length of a diagonal of the box whose length $l$ increase from $1\text{m/s}\text{to}2\text{m/s}$, width $w$ increase from $\text{2}\text{m/s}\text{to}2\text{m/s}$ and height $h$ decrease from $2\text{m/s}\text{to}3\text{m/s}$.