00:01
So in this question, they say, i'm on the surface, z equals f of xy, and my f of xy is equal to 4 plus x cubed, plus 3 y squared.
00:15
If i am at the point 2 comma negative a half, comma, 35 quarters, i want to know what is the minimum value of the directional derivative.
00:26
So the maximum value of the directional derivative i know is given by the magnitude of the gradient.
00:34
So if i want the minimum value of the directional derivative, i take the opposite, negative the magnitude of the gradient vector.
00:46
So let's get our gradient vector.
00:49
My gradient of f has what as its components? well, my partial of f with respect to x, that's just 3x squared.
00:59
My partial of f with respect to y, that's just 6y.
01:05
Now, i'm going to evaluate my gradient of f at the point that i was given.
01:13
2 comma, negative 1 1⁄2, and the z really doesn't matter this time, but it is 35 quarters...