I am a little confused about the gradient and etc.
I am able to compute the partials and figure out what the gradient vector is at a point. But say I get a question like "find the direction of greatest increase of f at a point (a,b)" should I just plug in the point (a,b) and then just make the gradient a unit vector, essentially eliminating the length aspect of it and only containing the directional aspect? Or if it asks "does f increase or decrease in the direction of the gradient at point (a,b)" do I just evaluate the gradient at that point and then find the magnitude of the gradient at that point, then the sign determines if it increases or decreases at that point.
Just want some clarification to make sure im reading the questions properly and computing the right things in certain situations. Im pretty comfortable with the gradient computations but sometimes its hard to know what they are asking for on a test or exam.
Any help would be appreciated,
thanks.