7.1 Functions of Two Variables – Surfaces and Level Curves

assigns a value based on 2 or more variables

It is a “double entry” function machine

Function of Two Variables

A function f of the two independent variables x and y is a rule that assigns to each ordered pair (x,y) in a given set D (the domain of f) exactly one real number, denoted by

Examples from Geometry:

#6 If , find f(1,2), f(-4,6) and specify the domain.

#8 If , find f(16,27), f(4,-1331) and specify the domain.

#12 If , find f(1,0), f(ln 2, 2) and specify domain

Describe the domain of the given function:

#18 #20

Application

#32 A manufacturer can produce scientific graphing calculators at a cost of $40 apiece and business calculators for $20 apiece.

a) Express the manufacturer’s total monthly production cost as a function of the number of graphing calculators and the number of business calculators produced.

b) Compute the total monthly cost if 500 scientific and 800 business calculators are produced.

c) The manufacturer wants to increase the output of scientific calculators by 50 a month from the level in part (b). What corresponding change should be made in the monthly output of business calculators so the total monthly cost will not change?

The following is an example of a Cobb-Douglas Production Function –

#34 The output at a certain factory is units, where K is the capital investment measured in Units of $1,000 and L is the size of the labor force measured in worker-hours.

a) Compute the output if the capital investment is $125,000 and the size of the labor force is 1,331 worker hours.

b) What will happen to the output in part a) if both the level of capital investment and the size of the labor force are cut in half?

Transparencies – pgs 517-521

Level Curve and families of level curves

Sketch the indicated level curve for each choice of constant C.

#24

#28

#30