Question: Consider the following function

\[f:{{R}^{2}}\to {{R}^{2}}\] \[f\left( x,y \right)=x{{e}^{y}}+{{x}^{2}}y\]

(a) We are interested in the point P(1, 0, 1) on the graph of f. In the direction of which unit vector \(\mathbf{u}\) does the function increases most rapidly?

(b) What is the absolute value of the directional derivative in the direction u you determined in (a)