00:01
This time, they give us the function f of xy is equal to y squared plus 2y to the 4x, and at the point 0 negative 2, the one is to compute the directional derivative and the direction from negative 4, actually that's the end point, and the start point is 0 negative 2.
00:22
So we're going to have to subtract.
00:24
So find the vector with that direction, that's negative 4.
00:26
And then let's see six and so if we want to find the magnitude to get the unit vector we'll end up with 16 plus 36 under a square root and that's just let's see square root of 52 that is equal to 2 square root 13 let's make sure for yep okay so our unit vector is actually going to be negative 2 over the square root of 13 and 2 over the square root of 13.
01:07
Now let's compute our gradient of our function.
01:10
And we'll get, let's see, with respect to x, 8y to the 4x, with respect to y, we'll end up with 2y plus 2e to the 4x.
01:32
And now let's compute the directional derivative.
01:38
We can pull out the 2 square root 13.
01:42
And we'll get, well, this will be positive, so let's compute this first...