Let F(x, Y) = $x ^ { 4 }$ - $y ^ { 2 }$

Let f(x, y) = $x ^ { 4 }$ - $y ^ { 2 }$ + $3 x ^ { 2 }$ + 2y - 7. The first partial derivatives of f(x, y) are zero at the points $( 0,1 )$ and $( - 1,1 )$ Use the second derivative test to determine the nature of f(x, y) at each of these points.

A) (0,1) neither relative maximum nor minimum, (-1, 1) maximum
B) (0, 1) relative maximum, (-1, 1) relative minimum
C) (0, 1) no conclusion possible, (-1, 1) minimum
D) (-1, 1) relative maximum, (0, 1) neither relative maximum nor minimum
E) none of these

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