Exercise 30

Use a graphing device as in Example 4 (or Newton’s method or solve numerically using a calculator or computer) to find the critical points of \(f(x, y) = 20e^{-x^2-y^2} \sin 3x \cos 3y\), \(|x| \le 1\), \(|y| \le 1\) correct to three decimal places. Then classify the critical points and find the highest or lowest points on the graph, if any.