MATH 1P97 Lecture Notes - Lecture 12: Saddle Point, Maxima And Minima, Second Order (Religious)

• School: Brock University
• Department: Mathematics and Statistics
• Course: MATH 1P97
• Professor: Sandra Yee

Document Summary

The variables x and y are called independent variables. Variable z, which is dependent on the values of x and y is the dependent variable. The domain of a function of two variables f ( x , y) is a set of ordered pairs of real numbers and may therefore be viewed as a subset of the xy-plane. Ordered pairs in the 3-d coordinate system can be represented by. Let f be the function defined by f ( x , y)=x+xy+ y2+2. Solution: f (0,0)=0+(0)(0)+02+2=2 f (1,2)=1+(1) (2)+22+2=9 f (2,1)=2+(2 )(1)+12+2=7 ( x, y ,z) We can visualize the graph of a function of two variables by using. The level curves of a function f of two variables are the curves with equations f(x,y)=k, where k is a constant in the range of f. As long as k<0 the graph is an eclipse.