The figure shows the level curves of a function $f(x,y)$ around a maximum or a minimum $M$. One of the points P or Q has coordinates $(x_1,y_1)$ and the other has coordinates $(x_2,y_2)$. Suppose $b > 0$ and $c > 0$. Consider the two linear approximations to $f$ given by $$\begin{array}{rcl} f(x,y) & \approx & a + b(x-x_1) + c(y-y_1), \\ f(x,y) & \approx & k + m(x-x_2) + n(y-y_2). \end{array}$$ (a) What is the relationship between the values of $a$ and $k$? A. $a = -k$ B. $a < k$ C. $a > k$ D. $a = k$ (b) What are the coordinates of point P? A. $(x_1,y_1)$ B. $(x_2,y_2)$ (c) Is M a maximum or a minimum? ? Maximum Minimum (d) Is the sign of $m$ positive or negative? ? Positive Negative (e) Is the sign of $n$ positive or negative? ? Positive Negative

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