Find a unit vector in the direction in which $f(x,y,z) = x/z + z/y^2$ increases most rapidly at $P(1,2,-2)$, and find the rate
of change of $f$ at $P$ in that direction.
$a^b$ means a raised to bth power. $2^3 = 8$.
A
unit vector in direction of most rapid increase:
$(-1/\sqrt{2}, 1/\sqrt{2},0)$ rate of change in direction of most rapid
increase: $1/\sqrt{2}$
B
unit vector in direction of most rapid increase:
$(-1/\sqrt{3}, 1/\sqrt{3}, 1/\sqrt{3})$ rate of change in direction of
most rapid increase: $1/\sqrt{3}$
C
unit vector in direction of most rapid increase:
$(1/\sqrt{2}, -1/\sqrt{2},0)$, rate of change in direction of most rapid
increase: $1/\sqrt{2}$
D
unit vector in direction of most rapid increase: $(-3/5,4/5,0)$ rate of change in
direction of most rapid increase: $1/5$
