Gradient is supposed to point in the direction of steepest ascent, but when I try to find the gradient of $f(x,y) = x^2 + y^2$ I get $(2x, 2y)$ and at $(0,0)$ this is $(0,0)$, but what does this gradient vector mean? When looking at $f(x,y)$ on a graph, I can see that any direction you go the graph will increase, so shouldn’t there be some direction the gradient points in?

  • 3
    $\begingroup$ Apparently, no. $\endgroup$ – Saucy O'Path Oct 28 '18 at 16:09

Of course not. The function $f$ has a minimum at $(0,0)$. So, you should expect that the gradient there is $(0,0)$.

  • $\begingroup$ I'm still a little bit confused, since I thought the gradient gives a direction to go for maximum increase, but the gradient isn't pointing anywhere in this example? $\endgroup$ – Ashton Halat Oct 28 '18 at 18:04
  • $\begingroup$ Wouldn't the gradient at least be pointing in any one direction since it is a minimum though? Wouldn't a minimum mean that the gradient should have some direction for the function to increase? $\endgroup$ – Ashton Halat Oct 28 '18 at 23:56
  • $\begingroup$ Which direction? It doesn't grow at that point. $\endgroup$ – José Carlos Santos Oct 28 '18 at 23:58

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.