(Solved): Given the function \( f(x, y)=x^{2}+x y+y^{2}+y \) a. List any critical points. b. State any relati ...

Given the function \( f(x, y)=x^{2}+x y+y^{2}+y \) a. List any critical points. b. State any relative maximum, minimum values or inflection points Show work used to identify critical points, relative extrema and inflection points. c. Graph the function with domain \( -2 \leq x \leq 2,-2 \leq y \leq 2 \) and include any relative max, min or inflection points in the graph. Attach graph.