A contour diagram for the smooth function $z=f(x,y)$ is shown below.

(a) Is $z$ an increasing or decreasing function of $x$? ? increasing decreasing
Of $y$? ? increasing decreasing

(b) Is $f_x$ positive or negative? ? positive negative
How about $f_y$? ? positive negative

(c) Is $f_{xx}$ positive or negative? ? positive negative
How about $f_{yy}$? ? positive negative

(d) In what direction does $\nabla f$ point at point $P$?
in the direction
(Give a vector that points generally in the right direction.)
In what direction does $\nabla f$ point at point $Q$?
in the direction
(Again, give a vector that points generally in the right direction.)

(e) Is $\nabla f$ longer at $P$ or at $Q$? ? P Q