WeBWorK Standalone Renderer

The surface $z = f(x,y)$ is shown in the diagram. The green point is $A = (-2,2,0)$ and the red point is $B = (2,2,0)$ .

(a) Are the following quantities positive, negative, or zero?

1. $f_y(B)$

2. $f_{xx}(A)$

3. $f_y(A)$

4. $f_x(B)$

5. $f_{yy}(A)$

6. $f_x(A)$

(b) Suppose a point $P$ in the xy-plane moves in a straight line from the green point $A$ to the red point $B$ .

1. Does the sign of $f_y(P)$ change from positive to negative, negative to positive, or is there no change in sign?

2. Does the sign of $f_x(P)$ change from positive to negative, negative to positive, or is there no change in sign?

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You can earn 50% partial credit for 4 - 5 correct answers, and 75% partial credit for 6 - 7 correct answers.