00:01
In this question, we're going to find the gradient of the function f of x, y equals y minus x at the given point.
00:09
Then, we're going to sketch our gradient together with the level curve that passes through the point.
00:16
Here we have f of x, y is equal to y minus x, and we are looking at the point 2, 1.
00:24
So first of all, what is the gradient of f? by definition, it is the vector consisting of the partial derivative of f with respect to x and the partial derivative of f with respect to y.
00:38
So what is my partial derivative of f with respect to x here? my partial with respect to x is just 0 minus 1, which is negative 1.
00:48
While my partial with respect to y, that is just 1.
00:54
Now, there's my gradient.
00:57
Now we're going to need the level curve that passes through this point.
01:02
So what do we do? well, we're going to figure out what f at the point is.
01:07
So f at 2, 1 is y minus x, so it's 1 minus 2.
01:15
That's equal to negative 1.
01:17
And so now, to get our level curve, we set our original function f of x, y equal to negative 1.
01:27
I am setting y minus x equal to negative 1...