Let f(x,y) - x^2y + xy^2. Find all vectors u such that Duf(1, -2) is exactly one-half the maximal possible directional derivative.
I assume you mean f(x,y)=
First find and . That norm [b]is[/tex] the "maximal possible directional derivative[/tex].
The directional derivative in the direction of vector is
Of course, is just the unit vector in the direction of and that can always be written as where is the angle makes with the x-axis.
That is, is any vector making angle with the x-axis where which is the same as .