I'm looking at this function $f(x,y) = a + ab^2$
The derivates would be:
$df(a,b) \over da$$= 1+b^2$
$df(a,b) \over db$$= 2ab$
Now from what I understand there are no stationary points, but could someone please explain the logic reasoning behind that? How can I reach the conclusion that there are not stationary points?
I'm thinking in equation 2 it's not possible to reach any conclusion because $a$ could be $0$ and then $b$ could be anything and vice versa.
In Equation 1 I assume because there are only one variable, it can be determined.
Is this reasoning correct and is there anything else that could be said regarding this?