# Thread: Terminology question: f(x,y) stationary points

1. ## Terminology question: f(x,y) stationary points

I have a question,

I saw the problem: "You have a function of two variables and know it's stationary points and you know if they are max, min or saddle points.

At which points is the function decreasing? At which points is it decreasing?

Is it right to say, a function of two variables is increasing towards it's maximum points and decreasing towards it's minimum points, it is decreasing and increasing at it's saddle points?

2. ## Re: Terminology question: f(x,y) stationary points

If you're asking about these things, I suppose you're not very familiar with directional derivatives and/or gradients. If your problem comes from a textbook or is part of one of your homework assignments, then these concepts are certainly explained in some of your material. If not, see
Directional derivative - Wikipedia, the free encyclopedia
Gradient - Wikipedia, the free encyclopedia

3. ## Re: Terminology question: f(x,y) stationary points

so I have to calculate the directional derivative through the stationary points?
If the directional derivative is positive it is decreasing, if its negative its increasing.

It that right?