(Solved): number 14 please Finding Local Extrema Find all the local maxima, local minima, and saddle points ...

number 14 please

Finding Local Extrema Find all the local maxima, local minima, and saddle points of the functions in Exercises 1-30. 1. \( f(x, y)=x^{2}+x y+y^{2}+3 x-3 y+4 \) 2. \( f(x, y)=2 x y-5 x^{2}-2 y^{2}+4 x+4 y-4 \) 3. \( f(x, y)=x^{2}+x y+3 x+2 y+5 \) 4. \( f(x, y)=5 x y-7 x^{2}+3 x-6 y+2 \) 5. \( f(x, y)=2 x y-x^{2}-2 y^{2}+3 x+4 \) 6. \( f(x, y)=x^{2}-4 x y+y^{2}+6 y+2 \) 7. \( f(x, y)=2 x^{2}+3 x y+4 y^{2}-5 x+2 y \) 8. \( f(x, y)=x^{2}-2 x y+2 y^{2}-2 x+2 y+1 \) 9. \( f(x, y)=x^{2}-y^{2}-2 x+4 y+6 \) 10. \( f(x, y)=x^{2}+2 x y \) 11. \( f(x, y)=\sqrt{56 x^{2}-8 y^{2}-16 x-31}+1-8 x \) 12. \( f(x, y)=1-\sqrt[3]{x^{2}+y^{2}} \) 13. \( f(x, y)=x^{3}-y^{3}-2 x y+6 \) 14. \( f(x, y)=x^{3}+3 x y+y^{3} \)