# Gradient of $f(x,y) = x^2 + y^2$ at $(0,0)$

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?

• Apparently, no. – 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 $$(0,0)$$.