I need to find the directions in which the directional
derivative of at the point has the value 1. I use the dot
product formula for directional derivatives where is a unit
vector; I set equal to one: The components of the gradient
vector: I plug in the coordinates: =1 , which is This tells me
that the where is the component of the unit vector in direction.
If I write the unit vector as I have . Now I have the elementary
system of equations: I not sure if the solutions for a,b the
correct components of the unit vector givng the direction
required. It makes sense to me, but I don't have the answer in
my book, so I can't check this.