What Do the Second Derivatives Tell You About the Graph $f ( x , y ) = 7 x ^ { 2 } + 1000 x y + 7 y ^ { 2 } - 3 x - 12 y + 18 ?$

Multiple Choice

What do the second derivatives tell you about the graph of $f ( x , y ) = 7 x ^ { 2 } + 1000 x y + 7 y ^ { 2 } - 3 x - 12 y + 18 ?$ Select all that apply.

A) Any critical point must be a saddle point.
B) There is a local minimum.
C) There are no local minima.
D) The function has a local maximum.
E) There are at least two local minima.