Find all the points at which the direction of fastest change of the function f(x, y) = x2 + y2 − 4x − 2y is i + j.

All the points that lie on the line:

Step-by-step explanation:

In order to find the maximum rate of change, we need to find the gradient of the function. The gradient of a function of two variables is defined to be:

So:

Hence:

Since we need to find all the points at which the direction of fastest change of the function is . Then:

Therefore:

So, we can conclude, that all the points where the direction of fastest change of lie on the line: