What Determines the Maximal Rate of Change for a Function at a Point?

[Saladsamurai]

I am given some function f(x,y) and I am asked to find what the maximal rate of change is at some point (x₀y₀) and the direction in which it occurs.

Is this correct: Maximal rate of change=$|\nabla{f}(x_0,y_0)|$

And for the direction, if $\nabla{f}(x_0,y_0)=<a\, ,b\,>$ then the direction is:

$$\frac{<a\, ,b\,>}{|\nabla{f}(x_0,y_0)|}$$

Thanks!

 

[Saladsamurai]

Just a yes or no will do me.

 

[Saladsamurai]

Here it comes!

 

[Dick]

You know |grad(f)| is correct answer, right? Rate is grad(f).u. Maximal rate is in the grad(f) direction, so u=grad(f)/|grad(f)|. Hence?

 

[Saladsamurai]

So my direction question is correct too. I just evaluate grad(f) and get some vector and then find the unit vector in that direction. Yes?

 

[Dick]

Yep.