Find the critical points of the following function. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. Confirm your results with a graphing utility. f left parenthesis x comma y right parenthesis equals x Superscript 4 Baseline plus 3 x squared left parenthesis y minus 2 right parenthesis plus 4 left parenthesis y minus 1 right parenthesis squaredf(x,y)=x4+3x2(y−2)+4(y−1)2 Question content area bottom Part 1 What are the critical points? enter your response here (Type an ordered pair. Use a comma to separate answers as needed.)

Question

Find the critical points of the following function. Use the Second Derivative Test to determine (if possible) whether each critical point corresponds to a local maximum, local minimum, or saddle point. Confirm your results with a graphing utility.

f left parenthesis x comma y right parenthesis equals x Superscript 4 Baseline plus 3 x squared left parenthesis y minus 2 right parenthesis plus 4 left parenthesis y minus 1 right parenthesis squaredf(x,y)=x4+3x2(y−2)+4(y−1)2