Exercise 29

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 \(f(x, y) = x^4 + y^3 - 3x^2 + y^2 + x - 2y + 1\) correct to three decimal places. Then classify the critical points and find the highest or lowest points on the graph, if any.