Final answer:
To find the maximum rate of change of f at the given point (2, 6), we need to find the partial derivatives of f(x, y) with respect to x and y, and then evaluate them at (2, 6). The partial derivative of f(x, y) with respect to x is 2x, and the partial derivative with respect to y is -2. Substituting x = 2 and y = 6 into the partial derivatives, we get the maximum rate of change: 4 and -2.
Step-by-step explanation:
The maximum rate of change of function, also known as the gradient, can be found using the partial derivatives of the function f(x, y). To find the maximum rate of change at the given point (2, 6), we need to find the partial derivatives of f(x, y) with respect to x and y, and then evaluate them at (2, 6).
The partial derivative of f(x, y) with respect to x is 2x, and the partial derivative with respect to y is -2.
Substituting x = 2 and y = 6 into the partial derivatives, we get the maximum rate of change: 2(2) = 4 and -2.