The level curves of a function f(x,y) is given in the image below.
I wish to determine the sign of the partial derivatives:
$f_{x} , f_{y} , f_{xx} , f_{yy} , f_{xy} , f_{yx}$
at the point P given in the image.
I am not sure how to solve this problem, never seen anything similar.
I imagine that the solution goes round the fact that the level curves values are reducing when x increases, so it must say something about the shape of the function and the slope that is being created, but I can't see how x or y creates the plane here, and definitely can't think of the second order derivatives.
Your help will be most appreciated, I find this problem interesting, as it's not technical, it demands understanding.
Best Answer
HINT
Observe that $P$ is on the curvee level $f(x,y)=6$ and $f(x,y)$ decreases for $x$ increasing thus
note also that from $P$ level curves are less dense with $x$ increasing thus