Example 72 Suppose we want to describe the elevation above see level of each point on the surface of a mountain For simplicity, suppose that the mountain just looks like a cone, with the base at sea level The altitude can be represented by the function \\begin{eqnarray*} fD & \longrightarrow & {\mathbb R} \\ z & = & f(x,y), \end{eqnarray*}\ associating to each point in theWhile technology is readily available to help us graph functions of two variables, there is still a paperandpencil approach that is useful to understand and master as it, combined with highquality graphics, gives one great insight into the behavior of a function This technique is known as sketching level curvesThe graph itself is drawn in an ( x, y, z) coordinate system Remark 2 Level curves of the same function with different values cannot intersect Remark 3 Level curves of utility functions are called indifference curves
Lecture Notes Chapter 1 1 C Contourlines Level Curves And 3d Graphs Pdf Pdf Function Mathematics Contour Line
