00:01
Okay, here we want to find the maximum rate of change of this double variable function at point minus 3 minus 2.
00:10
And the direction in which it occurs, the maximum rate of change, which is the direction of the gradient.
00:20
So basically the question wants us to calculate the gradient of this function and calculates the gradient of this function and calculates the norm or the length of the gradient of the gradient.
00:31
And as well as the direction of the gradient.
00:36
Right.
00:36
So the gradient, gradient f, is a vector, partial f, partial x, partial f, partial f, partial y.
00:46
This is a gradient, and so we basically want to know the gradient at x equals minus 3 and y equals minus 2.
00:56
So we first have a look, what is the gradient f? so partial f, partial x, align partial x partial f so we have x square plus y square over 2x the derivative of 2x which is a direct derivative of x square which is 2x so this is a x direction and we have on the y direction it's the same so this is gradient f so gradient f at x equal to minus 3 y equals minus 2 should equal to x square minus y square is 9 plus 4 which is 13, 2x which is minus 6, right? and 2y is minus 4 over 9 plus 4 again.
01:57
So this is a direction of the gradient and we want to normalize it in the end.
02:06
So let's not normalize it first.
02:14
So the direction is called n equals to, let's call this a and b...