Exercise 26

  1. Use a computer algebra system to solve the system of equations that arises in using Lagrange multipliers to maximize \(f(x, y, z) = x^2y^2z^2\) subject to the constraint \(x^2 + y^2 + z^2 = 1\).
  2. Solve the problem in part (a) with the aid of a graph and level surfaces. Use your CAS to solve the equations numerically. Compare your answers with those in part (a).