Final answer:
The linearization of the function z = f(x, y) at the point p(-3, 1) with given function values and derivatives is L(x, y) = 3 + 2(x + 3) + 3(y - 1).
Step-by-step explanation:
The question involves finding the linearization of a multivariable function z = f(x, y) at a point p(-3, 1). Given the details, the function value at the point is f(-3, 1) = 3, and the partial derivatives at that point are fx(-3, 1) = 2, and fy(-3, 1) = 3. The linearization L(x, y) of the function around the point p is given by:
L(x, y) = f(a, b) + fx(a, b)(x - a) + fy(a, b)(y - b)
By plugging in the given values, the linearization at point p(-3, 1) becomes:
L(x, y) = 3 + 2(x + 3) + 3(y - 1)