Chapter 14.5, Problem 62E

To determine

(a)

To calculate:

The gradient of $f$.

To determine

(b)

The value of $D_{u}f\left(1,1\right)$ and $D_{u}f\left(\sqrt{3},1\right)$.

To determine

(c)

To show:

the lines $y=mx$ for are level curves for $f$.

To determine

(d)

To verify:

$\nabla f_p$ is orthogonal to the level curve through $p$ for $p=\left(x,y\right)\ne \left(0,0\right)$.