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

question 61

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.

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