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The problem presented is asking for the signs of the partial derivatives \( f_x \) and \( f_y \) at the given points \( Q \), \( R \), \( S \) on a contour map of a function \( f \). The partial derivative \( f_x \) indicates how \( f \) changes with \( x \) while keeping \( y \) constant, and \( f_y \) represents how \( f \) changes with \( y \) while keeping \( x \) constant.

The signs of the partial derivatives can be inferred from the orientation of the contour lines and the gradient of the function, which points in the direction of the greatest increase of the function. The gradient is perpendicular to the contour lines and points towards higher function values.

(a) At point \( Q \):
- \( f_x \) is the change in \( f \) in the x-direction. Here, moving in the positive x-direction leads to lower function values since the contour lines indicate that we are moving from a higher contour line to a lower one (e.g., from 1 to 0.5). Thus, \( f_x \) is negative.
- \( f_y \) is the change in \( f \) in the y-direction. Again, moving in the positive y-direction leads to lower function values, meaning \( f_y \) is negative.

(b) At point \( R \):
- \( f_x \) is positive because moving in the positive x-direction moves from a lower to a higher contour line.
- \( f_y \) is positive because moving in the positive y-direction also moves from a lower to a higher contour line.

(c) At point \( S \):
- \( f_x \) is negative because moving in the positive x-direction moves from a higher to a lower contour line.
- \( f_y \) is positive because moving in the positive y-direction moves from a lower to a higher contour line.

To summarize:
(a) \( f_x \) is negative, and \( f_y \) is negative at point \( Q \).
(b) \( f_x \) is positive, and \( f_y \) is positive at point \( R \).
(c) \( f_x \) is negative, and \( f_y \) is positive at point \( S \).

(1 point) Determine the sign of fx and fy at each indicated point using the contour diagram of f shown below. (The point P is that in the first quadrant, at a positive
x and y value; Q through S are located clockwise from P, so that Q is at a positive x value and negative y, etc.)
(a) At point Q,
fx is ?
fy is ?
(b) At point R,
fx is ?
fy is ?
(c) At point S,
fx is ?
fy is ?
v and
v and
v and
