Direction of gradient vector in terms of partial

Asked Sep 25 '16 at 18:53

Active Sep 25 '16 at 19:08

Viewed 133 times

I am question regarding the direction of gradient vector. Why does it mean to say "gradient to be always pointing to to the maximum increasing direction"? From this https://math.stackexchange.com/a/222020/200649 I understand it will be max. magnitude.

But the direction whether increasing or decreasing should on partial derivatives? From what I can understand, gradient is just the partial derivatives of the function multiplied by unit vector in the direction intended. And this direction is in the direction of partial derivatives. But why it is the increasing direction of the function. Can't the partial derivatives point to the decreasing direction of the function.

What am I missing here?

edited Apr 13 '17 at 12:19

Community

asked Sep 25 '16 at 18:53

Abhishek Bhatia

1,758
7
23
38

Hello question. From this animation you can see that the slope of a line tangent to a surface at a point depends on which line you choose. The gradient will be parallel to the line with the steepest slope. – Sep 25 '16 at 19:00
Try the answers to this question. You might find them more illuminating. – amd Sep 25 '16 at 20:04

Direction of gradient vector in terms of partial

0 Answers0