The function f(x, y)has a local maximum at (-1, 1). What can you say (if anything)about the values of $f _ { x y } ( - 1,1 )$ ?
A)Nothing.
B)It is undefined or equal to zero.
C)It cannot be greater than zero.
D)It is equal to zero.

Question

Quizplus · Accepted Answer

The value of $f_{xy}(-1,1)$ does not directly inform us about the presence of a local maximum at the point (-1,1). The determination of a local maximum involves the second partial derivatives $f_{xx}$, $f_{yy}$, and the discriminant $D = f_{xx}f_{yy} - (f_{xy})^2$, not just $f_{xy}$ alone.

The Function F(x, Y)has a Local Maximum at (-1, 1) fxy(−1,1)f _ { x y } ( - 1,1 )fxy​(−1,1)

The Function F(x, Y)has a Local Maximum at (-1, 1) $f _ { x y } ( - 1,1 )$