chapter 36

Maxima, minima and saddle points for functions of two variables

Pages 10

If a relation between two real variables, x and y, is such that when x is given, y is determined, then y is said to be a function of x and is denoted by y = f (x); x is called the independent variable and y the dependent variable. If y = f (u, v), then y is a function of two independent variables u and v. For example, if, say, y = f (u, v) = 3u2 − 2v then when u = 2 and v= 1, y = 3(2)2 − 2(1) = 10. This may be written as f (2, 1) = 10. Similarly, if u = 1 and v= 4, f (1, 4) =−5.