Answer
$3$
Work Step by Step
Our aim is to take the first partial derivatives of the given function $f(x,y,z)$ with respect to $x$, by treating $y$ and $z$ as a constant, and vice versa:
$f_x(1,-1,2)=y+z=1$ and $ f_y(1,-1,2)=x+z=3$ and $f_z(1,-1,2)=x+y=0$
Now, the gradient equation is: $\nabla f (1,-1,2)= \lt 1,3,0 \gt$
The directional derivative at that direction is
$D_v f=\lt 1,3,0 \gt \times \dfrac{\lt 3,6, -2 \gt }{\sqrt {(3)^2+(6)^2+(-2)^2}} \gt=\lt 1,3,0 \gt \times=\lt \dfrac{3}{7}, \dfrac{6}{7}, \dfrac{-2}{7} \gt=3$
