A contour diagram for the smooth function $z = f(x,y)$ is given in the figure below. (a) Is $z$ an increasing or a decreasing function of $x$?   ? Increasing Decreasing (b) Is $z$ an increasing or a decreasing function of $y$? ? Increasing Decreasing (c) Is $f_{xx}$ positive or negative? ? Positive Negative (d) Is $f_{yy}$ positive or negative? ? Positive Negative (e) Is $\nabla f$ longer at point P or Q? ? P Q (f) If you were to sketch $\nabla f$ on the contour diagram at the point Q, how would it appear? Select all that apply. A. Parallel to the y-axis. B. Tangent to the contour at point Q. C. Parallel to the x-axis D. Points in the direction of increasing contour values. E. Perpendicular to the contour at point Q. F. Points in the direction of decreasing contour values.

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You can earn 50% partial credit for 3 - 5 correct answers.