00:01
We're given our function g at a particular point.
00:04
So we want to find a gradient of g at this point.
00:08
So we know that our gradient of g at the point 2 comma negative 1 is going to be equal to the partial derivative of g with respect to x, evaluated at 2 comma negative 1i, and that's going to be plus partial dirt of g with respect to y.
00:27
Evaluate a 2 comma negative 1, that's in the direction of j.
00:31
So the partial derivative g with respect to x is going to be y squared.
00:37
And the partial dirt of g with respect to y is going to be 2x y.
00:44
So now if we do the evaluation, we will get this is 1, so that's just i.
00:50
And that's going to be negative 4j.
00:54
So now we're asked to draw our gradient along with a level curve at the given point.
01:03
So we'll start with our x and y axis.
01:06
So the point is 2 comma negative 1...