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.