Question

Concerning directional derivatives, what is the maximum rate of change? In my notes I have the max value is the magnitude of the gradient, but i'm not sure if they're the same thing

Answer 1

the maximum rate of change is in the direction of the gradient... and that rate of change is the magnitude of gradient

Answer 2

Do you know how to calculate the magnitude of the gradient vector?

Answer 3

Yeah, so the gradient evaluated at some point is the direction, and the magnitude of the gradient is the max rate of change

Answer 4

yes.. the gradient vector points in the direction of the maximum rate of change and its magnitude is the max rate of change...

Answer 5

Thank you very much!

Answer 6

That's correct, it the surface isn't flat, then the gradient will have variable's x and y and you have to plug the values in to get the gradient at that point