For Each of the Following Functions, Find the Critical Point $f ( x , y ) = 4 x ^ { 2 } + 3 x - 5 y ^ { 2 } - 8 y + 7$

Essay

For each of the following functions, find the critical point, if there is one, and determine if it is a local maximum, local minimum, saddle point, or otherwise.(a) $f ( x , y ) = 4 x ^ { 2 } + 3 x - 5 y ^ { 2 } - 8 y + 7$ (b) $f ( x , y ) = - 2 x ^ { 2 } + 7 x - 7 y ^ { 2 } + 4 y + 9$ (c) $f ( x , y ) = 3 x ^ { 2 } - 5 y + 4 y ^ { 2 } + 12 x - 11$ (d) $f ( x , y ) = 2 y ^ { 2 } + 7 x + 17 y + 12$