Chapter 13, Problem 38CRP

a.

To determine

The gradient of $f\left(x,y\right)=y^2-x^2$ at $P_0\left(1,1\right)$ .

b.

To determine

The directional derivative of $f\left(x,y\right)=y^2-x^2$ in the direction of $P_0\left(1,1\right)$ toward the origin.

c.

To determine

The direction from $P_0\left(1,1\right)$ in which the directional derivative has the largest value and also find the magnitude of the largest directional derivative at $P_0\left(1,1\right)$ .