Exercise 48

Find the maximum and minimum values of \(f(x, y, z) = x^2 + y^2 + z^2\) subject to the given constraints. Use a computer algebra system to solve the system of equations that arises in using Lagrange multipliers. (If your CAS finds only one solution, you may need to use additional commands.) \(f(x, y, z) = x^2 + y^2 + z^2\); \(x^4 + y^4 + z^4 = 1\)