Final answer:
The gradient field of the function f(x, y, z) = x² + 4y² is (2x, 8y, 0).
Step-by-step explanation:
The gradient field of the function f(x, y, z) = x² + 4y² can be found by taking the partial derivatives of the function with respect to each variable. The gradient field is a vector field that shows the direction and magnitude of the gradient at each point in space. In this case, the gradient field is given by:
∇f(x, y, z) = (2x, 8y, 0)