Final answer:
To find f(x)(x, y) and f(y)(x, y) for the given function f(x, y) = 4xy + 4y³ + 4, we substitute x and y into the function. Then, we can substitute specific values for x and y to find f(x)(2, -1) and f(y)(-2, 3).
Step-by-step explanation:
To find f(x)(x, y) and f(y)(x, y) for the given function f(x, y) = 4xy + 4y³ + 4, we substitute x and y into the function.
Therefore, f(x)(x, y) = 4x(x) + 4(x)³ + 4 and f(y)(x, y) = 4xy + 4(y)³ + 4.
Next, to find f(x)(2, -1) and f(y)(-2, 3), we substitute x and y values into the respective functions:
f(x)(2, -1) = 4(2)(2) + 4(2)³ + 4 = 16 + 32 + 4 = 52
f(y)(-2, 3) = 4(-2)(3) + 4(3)³ + 4 = -24 + 108 + 4 = 88