The temperature model , where is the temperature in and is the pressure in pounds per square inch.

(a)

Graph:

(1) Draw the coordinate plane.

(2) Plot the points and connect the plotted points with smooth curve.

(b)

Apply derivative on each side with respect to .

.

The rate of chage of with respect to is .

Substitute in .

/lb/in².

When , /lb/in².

Substitute in .

/lb/in².

When , /lb/in².

(c)

The rate of chage of with respect to is .

Graph the function .

Observe the graph:

As tends to , approaches to .

.

The pressure increases rapidly, the rate of change in temperature remains constant.

As the pounds per square inch approaches infinity, the temperature will not change.

(a)

Graph:

(b)

When , /lb/in² and When , /lb/in².

(c)

Graph the function .

.

As the pounds per square inch approaches infinity, the temperature will not change.