That is correct up to the final step, and yes, you do then have to substitute in the point (2,0,–1).
Also, the magnitude of the rate of steepest descent is , because that is what you divided by in order to get a unit vector.
I just want to check that I am solving this correctly.
You are given a function and asked to find the directional derivative at the point in the direction of the steepest descent.
Partial Derivatives at :
Now this gives you the direction of the steepest descent : .
So you then find the unit vector:
And then you dot product the above with with the partial derivatives giving:
Is that the directional derivative? Or do I then have to substitute in the point ?
I would appreciate if someone could verify the above for me, or correct it (more likely!).
Also, is the magnitude of the rate of steepest descent ?
Thanks a lot.