Chapter 15.5, Problem 12E

Directional derivatives Consider the function $f\left(x,y\right)=2x^2+y^2$, whose graph is a paraboloid (see figure).

 a.    Fill in the table with the values of the directional derivative at the points (a, b) in the directions given by the unit vectors u, v, and w.

	(a,b) = (1,0)	(a,b) = (1,1)	(a,b) = (1,2)
$u=\langle 1,0\rangle$
$v=\langle \frac{\sqrt{2}}{2},\frac{\sqrt{2}}{2}\rangle$
$w=\langle 0,1\rangle$

b.    Interpret each of the directional derivatives computed in part (a) at the point (1, 0).