I am trying to find the local min/max and saddle points of the function: $f(x,y) = 9 - 2x + 4y - x^{2} - 4y^{2}$
This is what I have so far:
$f_{x}(x,y) = -2 - 2x = -2 (x + 1) \Rightarrow x + 1 = 0 \Rightarrow x = -1$
$f_{y}(x,y) = 4 - 8y = -4 (2y - 1) \Rightarrow 2y - 1 = 0 \Rightarrow y = 0.5$
Any ideas on how to proceed?